The Ghost of General Lee - S2-E6
Continuity mistake: When the bad guys from Sweetwater county try to steal Boss' safe, you see them pushing it up a ramp into the pickup truck. But in the next shot, when Daisy calls the operator, the safe is in the corner. And when Bo and Luke go to untie Daisy, the safe is gone.
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.
Deliberate mistake: Probably best for filming the scene, but Jennifer Hart pulls up and parks her car on the street on a red curb in front of an ambulance and walks away. (00:10:12)
Return of the Fighting 69th - S1-E6
Revealing mistake: Before Roxanne Trent hits the box, it is possible to see that her hand is normal, not iron. (00:17:01)