Oh man I could go on forever about this! I'll try to make a small list though, because I believe I may have a lot to say.
Of course, there's the classic alicorn OCs problem. Alicorn OCs are such a tough topic, because this community has so many of them. I really don't know why, but there's a lot of people who feel as if they think they should be 'the (now sixth) alicorn of the universe' but very few of them are ever incorporated very well. People using alicorns as their species for their ponysona makes me cringe every time. Unless there's some god or perfect human walking among us, none of us should have alicornism as none of us are perfect. Don't even get me started on "pegacorns" because those are just alicorns. You cannot tell me otherwise.
My solution: If you really truly feel the need to make an alicorn OC, just please put them in a place where they actually could be an alicorn. Right now there are only 5 known alicorns, so either make this one not known (easily by putting them in another place off of Equestria. There's so much unexplored area outside of Equestria, it should be incredibly easy) or put the alicorn in the future. All of my OCs, I like to think, are born past the whole mane 6 age of Equestria that seems to be the current age. It gives me an excuse to create technology and is fun to not have the mane 6 overpower whatever they feel. Creating an alicorn and putting them in the future would be placing them in undiscovered territory and could potentially work.
Red and black OCs are every artist's nightmare. Not entirely literally, but I can't stand them. Most of the time, they share the trait of alicorns too. Red and black OCs are such a clog on the eyes and are only made because people want to create hardcore OCs that they think can counter the lovable feminine world by being so hardcore! They're gross and are usually just created because people think they're cool, which they are not. I mostly see them with tragic hardcore backstories too, just to add to the effect of a totally metal pony. It just doesn't work, and no one will like it.
My solution: If you want to make a red and black OC, just please make it work. The famous Blackjack from Fallout: Equestria, Project Horizons, has a red and black mane, but has a white coat. Her design is pleasing to the eye because the red and black are not the dominant color choice. I think another excuse would be if the colors were not natural for a pony. Ponies can dye hair and fur, so why wouldn't this work? Hypocritically, I have a red and black OC, but his story goes like he's a tattoo artist and thinks red and black is cool, so he simply made himself red and black because he thinks he looks cool. (Zebra, so just white stripes to red)
Mary Sue OCs are every writer's nightmare. The biggest gripe is that these characters are unrelatable because they're perfect. No one can relate to a perfect character, because humans (and ponies) make mistakes. No one is perfect. People make mistakes, and people have weaknesses. Except for your OC apparently, which has no problems at all, is perfect in every way, and is loved and adored by everyone! In story writing, it creates no conflict or tension because the Mary Sue is already perfect, so the reader knows the character will be able to pass this obstacle with little to no effort. It's very boring and really turns people away from wanting to see more of the person's work. *yawn*
My solution: Just don't make them. If you suspect a character is getting to the Mary Sue level, just give them a weakness. If you are able to give a character a personal weakness rather than a physical one, that's so much better! A perfect personality is none-existent, and this would make great sense! High or low ego, not being as intelligent in easy fields, even just being scared is easy enough. It's hard to give a character a weakness, but it makes the character more realistic. Trust me, you'll love an imperfect character more than a perfect god. (And please, do we have to say Gary Sue? Why is Mary Sue a gendered thing? Just please don't)
The thing I may hate most above anything is tragic/dark backstories. My goodness, if I see even a hint of a bad backstory, I will have very little patience to keep reading. "Her parents died and her only sense of happiness in life is when she's asleep because it's the only time she isn't in constant agony. She hurts all the time too because she's so dark." No one can relate to that! No one wants to see something so dark in a world where magic is literally powered by friendship! Do I even need to point this out? It's just terrible. I believe people create backstories like these to 1. Create a character where the creator thinks they could fix them if they could just talk to them, which is just terrible, and 2. To make a hardcore pony. I've stated before, a hardcore pony feels weird and unnatural in the pony universe. Good luck making them fit.
My solution: If you write the story in an alright fashion, and not make it too dark, it can work, and I hesitate to say that. It's hard to do, but it is entirely possible to give an OC a dark backstory and still create a good OC. Let's say, a parent died. How did they die? Hit by a car...how dark is that? Slightly dark, but it's realistic. It can happen, and has happened. Now the character has to live their life with only one parent, but that is what made them who they are now. Because they lost their parent at an early age, they have trouble making friends for fear of losing them the same way, but then has this moment where they discover how lonely they have been and decides to stop fearing friends and embracing them. In a world that is fueled by friendship, this would be perfect! It's may be dark, but not too dark. People may relate because of how they may have lost something and have been scared since the day. There's more examples, but I'll leave your creative mind to think of them.
Something I really wish didn't exist is beautifully designed characters with crap stories. Characters that I wish I could have designed, but have such a rushed story. It's sad really. I believe this is because a person will overdesign a character and not think as to why they look the way they do. The beautiful character already sells me just from the design, but then feels fake as the story could have been put out through a random google search and answer.
My solution: Think about the character of the OC first. Who are they? Are they a pony who likes dogsled racing? Considering they need snow, they may like to wear winter clothing. Are they a scientist? I'm sure a scientist never enters a lab without a lab coat. It's easy! If you really want to design the character's looks first, then just think about why they would look that way. An insecure pony would not often try to look good naturally. (unless you are going for the stereotype of 'beautiful character doesn't think they're beautiful') A pony who is often drawn and seen in a dress may have the character of liking dresses. Easy!
The pony generator is controversial. Is that even a thing I have to tell people anymore? It's an easy way to make an OC, but is often just bad. Along with the anatomy not being entirely correct, most people make rushed OCs just to have an OC. Once these OCs are made, they'll use this pony generated pony as their icon and such, and you can tell. I hate seeing them. I can understand why people do this though; not everyone is Leonardo.
My solution: Because not everyone is Leonardo, I can see why people use this. The problem is that it's ugly. It makes for a great reference though! So why not just use it as a reference and ask someone to draw the OC for you? That way you'd have a good looking OC who is not clearly from the pony generator. Easy and simple!
Pure black or pure white colors on OCs is often not a subject that is talked about a lot, but it's something that needs to be said. Pure black or pure white is just, ugh. I can see it being ok in the eyes, as it's just that way. Being anywhere else, be it the coat, mane/tail, cutiemark, accessories, ect. is just obvious and not good looking. It's not a big problem, but it's still a problem I see a lot
My solution: Just make the black lighter and the white darker. Easy! What else do I need to say?
Bright pastel colors goes the same way. They are hard on the eyes and just hurt. Usually these colors are presets on some art programs (most often MS Paint) and are just easy to use. I encourage everybody to not use them though. in fact, don't use anything preset. Even backgrounds on phones and such, don't use presets. I hate them.
My solution: Just dull down the colors. It's better if you can make the colors match and work with each other. Another easy solution that doesn't need much explaining.
Mane and tails that don't match are just weird. Easy mistake, and easy fix. These lists are getting shorter and shorter because there's not much to say about them.
My solution: Just make them match. If one is braided, the other should at least look braidable.
Now, what exactly is a bad cutie mark? A bad cutie mark would be something that uses logos, number and/or letters, or just a common symbol used in everyday scenarios, such as a stop sign. Why do I not like these? Logos because it's such an easy route to take, numbers and/or letters because they shouldn't have to be something to read, and common symbols because they are often man-made (pony-made?) and just don't seem to work most of the time. A cutie mark should be something that, at the very least, hints at the pony's passion. It should be something simple but understandable. A firework? They probably like to make/launch fireworks.
My solution: Just find an easy alternative. If a pony may be smart, don't use a math equation or something, use a graduation cap or something. (I don't know what I associate with smart people, I'm sorry) Scientist? Don't use some theory or something, a beaker is just perfect! It may be harder, but the work is thousand times worth it.
I'm sure there's more, but I believe I've listed some of the major ones. I should also mention that these are just my opinions on the topics and are not an exact representation of what everyone thinks of your OC. No matter what people say about your OC, a good OC is only a character that you like. Just please consider these sort of stuff when making an OC, as I'm sure more people will be open to discussing or roleplaying with your OC. Thank you!