Awesomeness by Analysis: Izuku was able to figure out that Stain's quirk was blood-related and that his excessive use of blades and stabbing weapons are related before he even encounters him.
Bullying a Dragon: When a group of villains hold Izuku up as a hostage in hopes of detering heroes and cops from taking them down on the spot, unaware that at this point that Izuku is invincible.
Izuku: Look, I get it, you guys are villains, you're scary and you managed to get, like, halfway through a crime. Which is more than a lot of people can do these days, honestly[.] As much fun as this has been, I've got homework and I really don't have time to stick around.
Fantastically Indifferent: While Inko was understandably upset when Izuku started exhibiting strange behavior, coming home with money and getting involved in hero/villain battle, after the tenth time her reactions have tamed a bit.
Inko: Hey sweetie... Oh, another attack, hm?
Hero with Bad Publicity: When people started to see Izuku with the police (and riding in the back of their cars), Izuku had developed a reputation as a delinquent.
My Suit Is Also Super: Very much averted, as Izuku complains about the holes in his hoodie when a group of villains shoot him.
Izuku: Do you know how much these things COST!?
Noodle Incident: Kurobayashi was once a wrestler and was "overzealous" in saving money to propose to his then fiance.
Unluckily Lucky: The sheer number of times Izuku ends up stumbling into criminal activity (around ten in two weeks) is staggering. Luckily for him he's invincible at this point and while he gave up on being a hero, he's basically doing their job before the heroes can get a swing in. It gets to the point where Detective Tsukauchi think's he's doing it on purpose, this only being true in his hunt for the Hero Killer.
