Do the characters get any better?

he's still intelligent but he makes mistakes sometimes. I dont see that at as a problem, if fact is makes him more relatable. same as nana, shes really smart but she trips up a lot and admits to it. I'm really sick of the "genius" trope in anime which are always perfect and never wrong about anything

Think of it realistically. If your classmates started dissappearing the first thing that comes to your head won't be "oh! I think my classmate killed them!". And it was explained in the beginning how the talented were full of themselves and was ignorant towards others. So I doubt they'd take a moment to pay attention to the people around them.

And, if your frustrated with the characters being stupid, then you must have dropped Death note too.

My first thought would be "what the hell is happening?". Two people disappeared, someone almost "killed themself" and a third person got killed. (The person that almost got killed is also claiming that it wasn't just an accident)
They already considered the possibility of an enemy being there, they even "got it confirmed" when Nana stabbed herself. The realistic thing to do is ignoring all of this, right? Honestly, no matter how full of yourself you can be there's no way someone would ignore all of that.
Also the ones full of themself are the students, why is the teacher being that incompetent? "Yeah, let's not create panic and not tell the students that the disappeared people were probably killed". Personally I would prefer a little panic rather than risking the other's safety.

And sure, not all Death Note characters are super smart but really, they lived in a world where people don't know of the existence of the Death Note or even shinigamis. Realistically it would be almost impossible to get to the truth.
But these kids live in a world where they think they are being trained to defeat an all powerfull enemy. Am I really supposed to think it's normal that those students are stupid enough to not be more careful with their actions? At least they shouldn't leave the characters that can't defend themeself alone-

Also, sorry 1) for my butchered English, I'm Italian and 2) for getting a bit heated, I just read your answer with a really condescending tone, hope I didn't misunderstand.

I agree with you! As I said I actually do like Nana and Kyoya. I just didn't like the fact that 1) Kyoya made a correct theory with "proofs" but immediatly discarded it when Nana lied (without any proof) 2) Kyoya left the healer girl alone with the corpse. I know he probably wanted to investigate the room of the dead guy but Idk, a classmate just died and you leave him there? No calling the teacher? Nothing?
Other than that, he made some deductions that I wouldn't have done in a million years, he is really smart :)

I forgot to add that it's just plain impossible that someone would let a "yeah, he was probably just sick" be a good enough excuse for someone's death when there is no evidence. Props to Kyoya for not falling for it, but the situation in general was pretty dumb.

I think he just didn't want to turn his eyes off of nana, similar to how he acted when yuuka "died" sure he could have went around checking all the bodies and area but that would give nana time to possibly do something while he was distracted (like drop a phone) his instincts are pretty good as when she left to go back to tsunikichis room, she was going to dispose of the other photos under his bed.

a theory, no matter how convincing it may sound, is still just that, without physical evidence. he was a hair away from catching her he just needed that final confirmation.

In my original comment I asked if the characters get better because I only got to ep 6, I only read the first part of your comment to not get spoiled ^^
So sorry if you mentioned this but, in the episode he says that he wanted to check on the room but Nana got there before he was able to.
If he actually wanted to keep an eye on her I think he would have followed her to the room/he would have noticed she was going back to the storage after (or something like that) .I know I might be missing some information but please don't spoil me ^^
(Also, as I said, my problem isn't really with Kyoya, the boy is doing amazing. he is allowed some mistakes. I just want to know if the other characters get better)

i agree w this i hate the stereotype

._.