When I create a character, I look at characters I like. I ask myself the following questions after doing so:

"can this person fit here?"

"how do they react by fitting here?"

Then I look at their past: "what was one major event in their past, and how do they look if it turns out differently?"

And finally: "what can I give this person from my self, without making them a self-insert?"

These steps are not followed properly in the case of a new writer, who often fails to create a character who fits in with the setting, and instead makes a character that does not fit at all. For instance, let's say I write a COD fanfic. If my OC is from the future, is Tony Stark's niece, and is sooo badass that they can floor Soap? Does not fit.

Another thing that is often tossed aside is consideration for a character's place in a story. A character is there to interact with the world. It doesn't matter how good your characters are if you spend so little time on the background and the setting that you can't tell one city from another. If there even are cities, it might just be "generic location" which is very, very bad.

(which I'll get to in a moment), I think one of the biggest mistakes is being too nice or too mean to a character. Either they get all the things in life handed to them on a platter for no reason, or every bad thing to ever happen ever, again for no reason. You gotta strike a happy balance, which can vary depending on the setting— after all, (modern) fairy tale characters tend to get the 'happily ever after' more often than dystopian characters for a reason— and make your characters deserve/earn their punishments and rewards.

As for self-inserts, they can be done well, but the best-done SIs are the ones that are most representative of the author, not an idealized version.

Lemme drag one of my childhood make-believe selves out for a moment. She was shy, quiet, and liked to read, and was a little bit lazy, which is all fine and dandy until you also take into account that she looked human except for her yellow, slit-pupiled eyes, black leathery wings, spiky black tail, and ability to breathe fire. Did I mention she was half-Hungarian Horntail and hatched from an egg, and Charlie Weasley brought her home as a baby where she was raised as Ron's twin sister? ...I had weird fantasies as a kid.

Yeah, no. Don't go the 'ideal you' route. It hardly ever, if at all, ends well.

Anyway, there's my ten cents.

Probably making a character where the starting point and main aspect is the powers, or how cool they are, instead of the personality and suchlike!

I would say first and foremost putting too much of oneself in the character. A character should be a part of you, but not a thinly veiled you. This by its very nature leads itself to characters that if not outright Sues are certainly Sueish. But on a related not, too flawed is another very common one.

Those are the biggest ones in my opinion. Though there are certainly others.