Before completing V3, the background screen for the gallery menu will show one of the 16 students in their default sprite. After completing V3, the background can be Tsumugi with her mastermind eyes. The paint around the screen also changes colors.
Extra Fact: After the first chapter, you can get Shuichi without his hat. He can still appear with his hat, so you could get either version after chapter 1.
Possible Fact (?)
Monokuma and the Monokubs might only appear after completing the game. I was able to get both on my completed file but I checked over 500 (not exaggerating) times on my file where it’s not completed and they never appeared. I say possible because I might just be insanely unlucky. So they might appear beforehand and I just never got them…
The Monokub’s colors were chosen from the team members in The Super Sentai Series. There are also a few role similarities, like red being the leader and pink being the only girl.