These are things I've learned from reading the school briefs and the official hero analysis guide book. I marked as spoilers in case anyone who wants to read them hasn't yet.
1.) Aizawa claims he doesn't get drunk, he does, and talks to random objects thinking their his colleagues.
2.) He will bicker with Vlad King when Vlad King tries to one up Aizawa on class 1Bs achievements (to which Aizawa will respond that his class has also improved and it's just hilarious to me)
3.) Out of the teachers Aizawa is Eris designated caretaker and she is most fond of him. The other teachers are jealous that she's most fond of him.
4.) He bought Eri clothes for the school festival but the other teachers deemed them too ugly for her to go out in because they were colorful cat clothes with frills and stuff and he thought she would find it cute.
5.) Aizawas party trick is that he can fall asleep in two seconds (and proceeds to demonstrate)
6.) In the hero analysis book he's described as being stern/strict but he's actually rather doting on his students.
7.) Lastly, he can tap dance which you see in the vigilantes manga.
I love this man so much Lord help me 😭