I'll think on it. I might actually ask my writer because he might think of things I don't give he's more in that position himself. xD
At the end of the day you just want someone who is overall self improvement oriented, because what ever weaknesses they might have whether they're mental, physical or emotional will be overcome in time. But the question is then how do you decipher that it's a trait that's there. Might be something you could interview each other about, an obvious red flag is someone who lists no weaknesses. xD
I used to have a lot of trouble with criticism, but it was mostly that people weren't giving me explanations as to why something is wrong - so it can lead you astray sometimes and feel frustrated that nothing you do is ever good. The best weapon you have is to analyze everything and look for patterns. If your partner keeps pointing out some things, look for commonalities and ask them to be wordy with you where possible. You want them to explain exactly what's wrong and be as specific as possible, and then you need to offer the same in return.
Assertiveness is something I worked on a lot too personally. I used to have a very passive style of communication (still do sometimes depending on the context) but one thing that helps as well is over time you get comfortable with people and you can get to a point of hurling insults even if you want knowing neither of you take it seriously. But it's still not always true with all friends, I think what matters most is if you can tell where the person is rebuffing advice for feedback on behaviour or acknowledging it's something they do. A lot of the times people fight it's out of pure miscommunication and they actually agree, they just didn't think they do. So being mindful of how you present arguments and even then, just explaining what you perceive of the other person goes a LONG way.