Continuity mistake: "Railway Station" (Adventure 2, Part 4): Steel's crooked bow tie straightens itself out between takes as he's confronting the soldier's ghost. (00:04:00)
Coming Home - S1-E13
Plot hole: The logistics of the episode don't really make sense; Amuro's home village is held by (literally) a handful of Earth soldiers cut from their main force and that spend their time getting drunk and acting as occupation force, but Zeon has a full base (again, literally, almost) next door that sends reconnaissance troops and even aircraft to check for any activity at the refugee camp. There's no reason why the undisciplined and free soldiers would stay in such a dangerous position where they could be wiped out by overwhelming forces anytime, nor why Zeon would keep a pocket of the enemy forces that they can crush with ridiculous ease.
Planet of the Slave Girls - S1-E2
Continuity mistake: When Buck goes to run out of the door of the factory, it's a solid door, with a bar-type handle. When the scene shifts to the outside, the door he runs out of leads directly inside, but the door has vent slats on the lower half, and the handle is completely different.