Background changes when LeBeau explains why they should buy from the vegetable peddler.
The amount of champagne in Colonel Klink's glass keeps changing while he is talking to Fraulein Ziegler.
During the introduction, when the vendor points to the cucumber with the message, it is different and in a different position than the one Carter grabs (which he finds out was meant for Hogan).
Colonel Hogan tells Klink that the Me 110 has no maneuverability with a bomb load. In fact, the Me 110 had poor maneuverability even without bombs, and was no match for Allied single-engine fighters.
Field Marshall Kesselring's car has the steering wheel on the right side. In Germany, the cars would have the steering wheel on the left side.
In the introduction, when the vendor enters the gates, there are already wheel tracks from the cart on the ground, indicating there were multiple 'takes' of the sequence.
When Hogan and Schultz go to visit Klink in his cell, the cell door is not even latched. This is obvious by looking at the door frame of the cell. The latch should be visible through the hole in the cell door frame, but is not. When Schultz is supposed to be unlocking the cell, he does not even turn the key, and the latch does not move - but then, the latch did not need to move because it was never latched in the first place (assuming there is even a latch in the cell door).
When Schultz comes in to invite the gang to a cocktail party, the view changes from Hogan and Schultz to Kinchloe and Carter (standing) with Newkirk and LeBeau seated at the table. When Kinchloe walks toward Schultz, asking if the party is the bash for Field Marshal Kesselring, it appears that the shadow of the microphone crosses the side of Kinchloe's forehead.
In some instances, there is a reflection of the production lights in Klink's monocle.
There is no explanation as to who the peddler is, nor why he is bringing a message to Hogan inside the Stalag to be delivered to the underground who are outside of the compound. Logic would suggest that he give the message directly to the underground.
It is winter in Germany which is under frequent aerial bombardment. It is never explained how a street peddler has acquired cucumbers and tomatoes as well as a variety other of fresh produce.
A peddler arrives at Stalag 13 pushing a cart laden with produce he wishes to sell. There is no clarification as to where he came from, nor where he is headed when he departs the camp with his pushcart. The nearest town has been variously described as being miles away.
Hogan describes the information the vegetable/fruit peddler is passing on as 'production figures for the Luftwaffe' - no indication of what specific materiel the production figures refer to as being produced. Hogan tells LeBeau to pass it on to the Underground. It would make more sense that London would be interested in that kind of information than the Underground.