Plot hole: This episode revolves around training the reluctant, untalented Schultz to impersonate Klink to get the captured heroes back from the Gestapo. This is actually a pretty common theme, somebody, usually one of the heroes, impersonating an officer to free a prisoner. The plot gives no reason why this time, they would have to use the cowardly, untalented Schultz instead of doing it themselves.
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.
Plot hole: The Heroes take an empty oil drum to the depot, knowing full well that Schulz will protest, allowing them to steal a full one. However, all but their barrel have snow on it. Since it's really salt, it all falls off as they load it on the cart. With real snow, that wouldn't happen. It would be quite obvious that the barrel they are taking out is not the one they brought in.
Plot hole: Hogan's men steal the motor from the silent plane. When Klink and Burkhalter inspect the plane, Burkhalter doesn't notice the engine missing. Later Klink doesn't notice the fact that it has been put back. This is totally impossible for two reasons: Firstly, if a propeller airplane misses its motor, there is no place to mount the propeller. Secondly, when we get to see the whole plane, it becomes obvious that it has an open engine cowling which leaves the motor exposed to be cooled by the airstream. The propeller issue aside, if there is enough light to see the hand in front of your eyes, it is impossible to miss either the presence or the absence of an engine inside that kind of cowling. Add to this the fact that both Klink and Burkhalter are Luftwaffe (Air Force) officers and therefore by trade have some experience with airplanes, the whole thing becomes even more ridiculous.