Some of Koro-sensei's weaknesses can be inferred or justified by his personality, actions, or another weakness.
Weakness 12: Getting wet. During a particularly humid day, his head absorbed the moisture in the air and swelled up. A later chapter reveals Weakness 23: He canít swim. His entire body will swell up when exposed to water.
Weakness 29: He gets carried away by official positions, where he took his role as the jailer during the Cops and Robbers game way too seriously. Earlier, Koro-sensei also played the role of a hot-blooded baseball coach and an overly strict lifeguard (Weakness 22: Heís very strict about poolside manner) to the same degree. But what's Koro-sensei's official job, you know, the one that he's really good at and the primary motivation behind playing all of the above positions so well? Being Class-E's homeroom teacher.
Nagisa is always wearing two thin, black bracelets around his wrists. After Chapter 112's reveal, it's safe to assume that they're actually back up hair ties. He really doesn't want to be seen in public with his long hair down.
During the intro to the Hotel Arc, the mastermind demands that Nagisa and Kayano trade off Koro-sensei for the antidote. Karasuma considers complying, despite the risk of a worst case scenario where both kids are kidnapped and the antidote is never handed over, but eventually decides against it. After reading the entirety of the arc, you'll realize just how horrific the actual "worst case scenario" would've turned out:
As detailed during The Reveal, Kayano and Koro-sensei would have been restrained and buried together in anti-sensei material and cement. Koro-sensei could either escape by exploding, killing Kayano in the process, or save her life by sacrificing himself and succumbing to the anti-material. Though there's no guarantee that the second option would've been explosion free...
Meanwhile, the same events would've occurred for Nagisa: Takaoka would have trapped him on the heliport and blown up the antidote, sending Nagisa spiraling into his Unstoppable Rage—except Terasaka wouldn't have been there to throw him the stun gun and snap him out of his bloodlust. Without a clear head and the second weapon, Nagisa would not have been able to utilize the secret technique, rendering him powerless to stop Takaoka from murdering him.