Plot hole: When Henry and Ellie are cornered in the launch tower during the 'Toppat Recruits' and 'Pardoned Pals' routes, the former goes back in time so that the soldiers that apprehended them were never recruited and therefore the main characters are no longer cornered in the present. However, this should simply cause different people to try to stop them, not an entire removal of the threat.
Factual error: In 'Escaping the Prison', the description for the Opacitator says that it will turn you opaque, allowing you to pass through walls. 2 problems. First, opaque is the opposite of transparent (see through), despite what the description claims. Also, the transparency of objects only affect how much light passes through them, it doesn't affect any other physics (a glass can't go through walls just because it is transparent). Even if the device did make objects opaque, it would not affect any physics or have any effect on Henry.
Other mistake: In the 'Valiant Hero' ending to 'Completing the Mission', Charles is killed when the space station he is in explodes. Somehow, his headphones survive the explosion that the space station and Charles himself didn't (they are found on his grave at the end).
Suggested correction: Who's to say that the headphones on the grave wasn't a copy or a similar one of the one he was wearing? We never see anyone return to where the ship exploded, so we don't know anything, hence it can not be considered a mistake.
Audio problem: In 'Fleeing the Complex', there is an ending called 'Presumed Dead'. Towards the end of this route, Henry is told that he is the first person to have escaped The Wall. As he is told this however, the person speaking is not moving his mouth.
Suggested correction: Dimitri's mouth was deliberately concealed at that shot, due to him being too small on the screen at that time for the animators to consider adding details. Now, it wouldn't have looked as good if it weren't for his beard.
Then that's also a deliberate mistake.
