Found another two
If your champion has all your traits picked, and you level him up again, and you go to pick another level, the game won't let you get out of the screen.
I did not test whether you could end turn without picking a level.
I would suggest creating a dump trait that you can pick that just gives something tiny and is repeatable to avoid this, or implementing a level cap for heroes that's individualized to the max level of each hero. (In other words, max level= number of traits you can pick+1)
One of the weak dungeons (the one with the skull castle icon), has to be landed on twice for the quest to spawn.