Maybe you like anime, maybe you don't. What are some of your least favorite parts you could do without?

I personally am not a big fan of melodrama, which is problematic because it seems like Japan's preferred method of storytelling and they love to overact the shit out of all kinds of stuff. This often goes hand in hand with super cliche voice types (squeaky girls, tryhard coolguys, timid everyguys, bullhorn yellers, etc) that can really grate on my ears. My favorite anime tend to be ones that keep anime cliches to a minimum.

What about you guys?

Love triangles. Fuck all of them. Just let the obvious lovers have their happy ending damn you.

They are not hand drawn anymore. They don't make stuff like Megazone 23, Madox 01, Angel Cop, Black Magic M66, Wicked City, Bubblegum Crisis, or 80s Cyberpunk anymore. The detailed hand-drawn art is gone. Film grain added depth to a picture. I feel most stuff is overly simple looking or too cartoonish or horny. All this Shonnen shit is just that, shit.

Filler.

Daddy issues.
The father often seems to have walked the same path as the protagonist. Or turns out to be crucially important to the plot and the puppetmaster behind a lot of things/people. The father has the same talents and sort of friends the protagonist has. The older generation seems to be a copy of the younger one, and not actual individuals. The father is mysterious and aloof, emotionally unavailable and his actions of the past are often emotionally scarring for the protagonist. Sins of the father: the protagonist has to make right what his father started but could not finish. Or he has to make right what his father made wrong.

I watch a lot of anime, and there are many things that annoy me about them. But Western tv shows often have even worse annoyances.

Anime tend to get a low rating from me when I simply detest the main characters. For example an overaggressive tsundere, or a pathetic MC that never tries to get better.

Other annoyances include whispers that the viewer can't hear.

Or overly sexualized characters without showing nudity. (like if you go that far, why not? )

Or massive plotholes.

Or massive flashback arcs.

I could go on, but overall my experience with anime is obviously positive, so I don't want to be too negative.

Fillers

and

having to wait a week to watch one bloody episode if its a good anime lol.

and 

the sudden delay to next week that only shows up on that day.

All of those reasons are why I keep a backlog, and wait until an anime season is completed entirely. On a related note I dislike cliffhangers!

There's a lot I like about anime but also a lot that I dislike.

Currently I'm pissed off about the sheer amount of manga adaptations that never get more than one season even though there's already enough material for more seasons.
That's basically the reason why I still buy mangas. I can get the full content and not just the first arc.
But the studios rather convert every manga in existence into anime and hope that one of them is a mega ultra hit instead of sticking with one til the end.
It's really hard getting excited for a new anime when you know there's a good chance that there won't be a second season.

Also, not enough people of color. Yep, I'm gonna be "that guy," he was bound to show up sooner or later so don't act surprised. :p

It's just astounding to me how you can have people with pink, green, purple hair walking around like it's totally normal, women with unrealistic proportions and curves that Japanese women don't typically have, guys with the physical strength of an elephant that's simply impossible, but adding a few people of color is simply too much to ask.

It's not a big deal and I'll live without it, but having more diversity in anime would be nice, seeing as how anime is huge in the black community anyway.  That's why I applaud shows like Cowboy Bebop that try to be inclusive.