Let's start with an actual definition. For simplicity, I'm using Wiki's.

"A Mary Sue is an idealized and seemingly perfect fictional character. Often, this character is recognized as an author insert or wish fulfillment. They can usually perform better at tasks than should be possible given the amount of training or experience. Sometimes, the name is reserved only for women, but more often the name is used for both genders. A male can also be referred to as a Marty Sue or Gary Stu, but Mary Sue is used more commonly."

So taking what you stated in the opening post, yes that view point does fit this definition. However, is your opening statement valid or bias?

1. fighter, mechanic, speak droid, pilot falcon (better than Han).

She was orphaned on a Jakku as a very young child under the ownership of junk dealer. While its not spelled out fully in the movie, its not too hard to envision what her life would have been like. She clearly would have had a hard life and would have required to either learn how to take care of herself or be taken advantage of always. Considering when we see her she is clearly healthy, agile, able to fight, and defend herself I posit that it is obvious this life taught her how to fight. Additionally, as proven in other movies, young force wielders will use force to assist them without their knowledge. Surely this has helped her reflexes and responses as well.

Being owned by a junk dealer it's also pretty obvious that, similar to Anakin, this life allowed her time to really get to know how to be a mechanic. Clearly that is her saving grace as she uses those skills to survive. She knows technology and can repair it successfully to remain healthy as demonstrated pretty clearly in TFA.

Speaking droid. Why is this some kind of oddity? It seems pretty obvious that interacting with droids is pretty common place in SW universe. Given her life in Jakku as such, I don't see how it could be perceived she wouldn't have learned how to interact with several 'languages'. Similar to Europeans. 

The Falcon was owned by her owner. She knew it was an old "junk" ship and clearly along with her already demonstrated mechanical skills, she was able to recognize what was good/bad about it. Given that every single other major character in SW easily flies any ship, I don't think its hard to conclude she could as well with her past. I also don't see how you can conclude she understands the Falcon better than Han. She did not do anything as a pilot or mechanic better than he did. She did repeat or acknowledge issues that he also knew and that was about it.

Fact is, her very hard life as a junk shop owner's property easily explains all the four topics. Problem is the movie couldn't go into detail as it has to expect the viewer can infer this info out of what it does show. This is no different than Luke actually. 

2. Force use better than Kylo.

That's complete BS and its so annoying how people keep repeating this. Its like you all don't actually pay attention to what's going on in the movie. Kylo Ren is very powerful in the Force. There is no question about that. However, he wasn't a master. He was still being trained. He also, like Anakin and Luke, was significantly mentally and emotionally fucked up. She also is clearly very powerful. Very likely as much as Kylo, just untrained and hasn't really figured it out yet. He clearly overwhelms her without any effort on Takodana. Then he peaks into her mind and realizes that she is very powerful. This actually startled him as he wasn't expecting it and his own narrative to Snoke states this exactly. She also was just told pretty much the same stuff Anakin and Luke were told when they were first starting to interact with the Force and as he is once again peering into her mind. So her ability to recognize that and sort of use it, is more like raw talent some people have for music / art / etc than it is miraculous as some of you preach.

Using the Force requires mind control and emotional stability. At the end of the movie Kylo is anything but stable. He's critically hurt but is using his own power to keep himself going as well as emotionally fucked and no where near stable due to just murdering his father. Which he was deeply struggling with and conflicted about. This is the ONLY reason why she was able to get a lucky hit and best him. Re-watch the ending. She did not demonstrate she was better. She was knocked out early, came out and barely defended herself until she had her own moment of quality similar to the few moments Luke did well during his first fight with Vader. (even though Vader was mostly toying with him in these scenes) 

In TLJ she had now been working with Luke and had been focused on bettering her already good skills with staffs etc that translate well to light saber. She also had focused a lot on basic Force controls. Yet she still had nothing on anyone in Snokes chamber. The only amazing Force moves here were Snoke and Kylo. Though she handled herself nicely in fighting which makes sense due to her life and defined skill set in TFA.

3. Folks like her. 

Umm so what? People liked Anakin, Luke, etc. She's a nice person and passionate about helping. People liked and quickly started to follow Jyn Erso relatively quickly as well for similar reasons. Like it or not, she is a hero of this trilogy and is being characterized as such. No different than any other hero character.

4. Summary

She is not a Mary Sue. She is not "seemingly perfect". She has failed many times and is not better in force/etc than obviously more advanced characters like Kylo. Her entire character makes sense when you get over petty bias' and pay attention to the deeper surrounding story. Her basic premise is no different than Anakin, Luke, Jyn, etc. 

5. My Rant.

My opinion is that folks will always bitch about SW when its not molded to fit exactly like the original trilogy. Any creativity to open up the universe more is met with crazy fanaticism because the movie didn't fit their personal ideas of what SW is supposed to be like. We all envisioned what young Anakin/Vader would be and couldn't accept anything different. We all envisioned what Master Luke would be like post RofJ and anything different has to be wrong and horrible. All the while completely ignoring any story plot issues, stupid jokes, and meh characterization present in the original trilogy.

SW is arguably the best saga ever created. Enjoy it instead of trying to force it to fit your personal bias.

Let's start with an actual definition. For simplicity, I'm using Wiki's.

"A Mary Sue is an idealized and seemingly perfect fictional character. Often, this character is recognized as an author insert or wish fulfillment. They can usually perform better at tasks than should be possible given the amount of training or experience. Sometimes, the name is reserved only for women, but more often the name is used for both genders. A male can also be referred to as a Marty Sue or Gary Stu, but Mary Sue is used more commonly."

So taking what you stated in the opening post, yes that view point does fit this definition. However, is your opening statement valid or bias?

1. fighter, mechanic, speak droid, pilot falcon (better than Han).

She was orphaned on a Jakku as a very young child under the ownership of junk dealer. While its not spelled out fully in the movie, its not too hard to envision what her life would have been like. She clearly would have had a hard life and would have required to either learn how to take care of herself or be taken advantage of always. Considering when we see her she is clearly healthy, agile, able to fight, and defend herself I posit that it is obvious this life taught her how to fight. Additionally, as proven in other movies, young force wielders will use force to assist them without their knowledge. Surely this has helped her reflexes and responses as well.

Being owned by a junk dealer it's also pretty obvious that, similar to Anakin, this life allowed her time to really get to know how to be a mechanic. Clearly that is her saving grace as she uses those skills to survive. She knows technology and can repair it successfully to remain healthy as demonstrated pretty clearly in TFA.

Speaking droid. Why is this some kind of oddity? It seems pretty obvious that interacting with droids is pretty common place in SW universe. Given her life in Jakku as such, I don't see how it could be perceived she wouldn't have learned how to interact with several 'languages'. Similar to Europeans. 

The Falcon was owned by her owner. She knew it was an old "junk" ship and clearly along with her already demonstrated mechanical skills, she was able to recognize what was good/bad about it. Given that every single other major character in SW easily flies any ship, I don't think its hard to conclude she could as well with her past. I also don't see how you can conclude she understands the Falcon better than Han. She did not do anything as a pilot or mechanic better than he did. She did repeat or acknowledge issues that he also knew and that was about it.

Fact is, her very hard life as a junk shop owner's property easily explains all the four topics. Problem is the movie couldn't go into detail as it has to expect the viewer can infer this info out of what it does show. This is no different than Luke actually. 

2. Force use better than Kylo.

That's complete BS and its so annoying how people keep repeating this. Its like you all don't actually pay attention to what's going on in the movie. Kylo Ren is very powerful in the Force. There is no question about that. However, he wasn't a master. He was still being trained. He also, like Anakin and Luke, was significantly mentally and emotionally fucked up. She also is clearly very powerful. Very likely as much as Kylo, just untrained and hasn't really figured it out yet. He clearly overwhelms her without any effort on Takodana. Then he peaks into her mind and realizes that she is very powerful. This actually startled him as he wasn't expecting it and his own narrative to Snoke states this exactly. She also was just told pretty much the same stuff Anakin and Luke were told when they were first starting to interact with the Force and as he is once again peering into her mind. So her ability to recognize that and sort of use it, is more like raw talent some people have for music / art / etc than it is miraculous as some of you preach.

Using the Force requires mind control and emotional stability. At the end of the movie Kylo is anything but stable. He's critically hurt but is using his own power to keep himself going as well as emotionally fucked and no where near stable due to just murdering his father. Which he was deeply struggling with and conflicted about. This is the ONLY reason why she was able to get a lucky hit and best him. Re-watch the ending. She did not demonstrate she was better. She was knocked out early, came out and barely defended herself until she had her own moment of quality similar to the few moments Luke did well during his first fight with Vader. (even though Vader was mostly toying with him in these scenes) 

In TLJ she had now been working with Luke and had been focused on bettering her already good skills with staffs etc that translate well to light saber. She also had focused a lot on basic Force controls. Yet she still had nothing on anyone in Snokes chamber. The only amazing Force moves here were Snoke and Kylo. Though she handled herself nicely in fighting which makes sense due to her life and defined skill set in TFA.

3. Folks like her. 

Umm so what? People liked Anakin, Luke, etc. She's a nice person and passionate about helping. People liked and quickly started to follow Jyn Erso relatively quickly as well for similar reasons. Like it or not, she is a hero of this trilogy and is being characterized as such. No different than any other hero character.

4. Summary

She is not a Mary Sue. She is not "seemingly perfect". She has failed many times and is not better in force/etc than obviously more advanced characters like Kylo. Her entire character makes sense when you get over petty bias' and pay attention to the deeper surrounding story. Her basic premise is no different than Anakin, Luke, Jyn, etc. 

5. My Rant.

My opinion is that folks will always bitch about SW when its not molded to fit exactly like the original trilogy. Any creativity to open up the universe more is met with crazy fanaticism because the movie didn't fit their personal ideas of what SW is supposed to be like. We all envisioned what young Anakin/Vader would be and couldn't accept anything different. We all envisioned what Master Luke would be like post RofJ and anything different has to be wrong and horrible. All the while completely ignoring any story plot issues, stupid jokes, and meh characterization present in the original trilogy.

SW is arguably the best saga ever created. Enjoy it instead of trying to force it to fit your personal bias.

It would be interesting to read about that many times she failed.

Reys failures

She opens the wrong door and lets the Rathtars out, almost getting everyone killed

Shes the only person we see miss a shot with her blaster in TFA

She refuses the call, runs into the forest and loses/gets captured by Kylo

She “goes to the dark place” when reaching out to the force, which causes Luke to be reluctant to train her

She fails to convince Luke to join the cause

She fails to turn Kylo Ren which would have cost her life had Kylo not saved her.

What were the consecuences?