Plot hole: We see Hogan's men empty out the gunpowder from a lot of cartridges inside the armoury. What did they do with their empties? It's not like a mound of empty cartridge cases on the ground wouldn't draw some suspicion is it? Yes, I am aware some options come to mind, e.g. putting the bullets back in and stuffing them back into the belts, but none of that is actually shown or talked about - LeBeau even chucks one cartridge over his shoulder, implying they are not very concerned about hiding their tracks.
Character mistake: The artillery officer asks "Does headquarters expect a squad of infantry to replace experienced artillery men?" Hogan only offered "his detachment", and he's wearing a Luftwaffe uniform (and so is LeBeau). Why does the artillery officer get the idea that the "detachment" would be infantry, that is to say, ground forces (Heer) troops? To avoid confusion: Yes, the Luftwaffe did have infantry units, but those would be viewed by other branches as Luftwaffe guards primarily, not as infantry.