This video has to be one the best examples of this.  The production value is super low the lip syncing is hilarious, and the lead singer was high when the video was shot, and he is chewing imaginary gum.  Originally this song was intended to be a duet with Chaka Khan.  I'm sure the video would have had a higher production value if she would have sung in it, but it might have almost as bad since she had drug issues during that time also and maybe both people in the video would have been high at the same time.

The parody barely changes stuff up:

Unintentionally (or is it?) funny and yet unexpectedly good too: 

More intentional but I felt like sharing it anyway:

Peak Soviet music, they didn't even need consonants over there 

This is the one that came to my mind.  Maybe I'll think of some others.  I watched a lot of MTV back in the day.

Technotronic - Pump Up the Jam. Looks nowadays like a 4-year old got hold of the video editing software and played around for 15 minutes:µ

https://www.youtube.com/watch?v=9EcjWd-O4jI

But Ace of Base managed to do even worse than that:

https://www.youtube.com/watch?v=8G-wu5F3ROs

Also, they absolutely abuse greenscreens until psychedelic becomes hilarious:

https://www.youtube.com/watch?v=wh-07BzfgYY

Heh, Pump Up the Jam is a really catchy song with a really stupid video.

This one has a much higher production value than the first one I posted.  The silly dancing and hilarious costumes make it unintentionally funny.