Right after Hogan and Klink go back to Klink's guests in his quarters and Klink does not have his monocle, the Major, who is holding a glass in his left hand, stands up to talk to Klink and Hogan. When the camera changes its angle, Klink now has his monocle again, and the Major is holding his glass in his right hand.
In Klink's quarters, right after Klink and Hogan finished talking privately, Klink's trademark monocle is briefly missing.
When the gang is planting the explosives in the bridge, Carter is taping his charge to the bridge support. When he finishes taping it, there is a cut to a shot of Carter, Buckles, and Kinchloe in the background. Carter asks Kinch if he is ready, to which he replies affirmatively. There is a cut to a wider shot from Carter's right side, showing the whole gang (including Buckles) working on the explosives - however, the detonator is now in the charge Carter and Buckles are working on. There is a cut to Hogan ordering the crew to fire their rifles, then a cut back to the same wide shot showing the gang reacting to the rifle fire. During the reaction shot, the detonator wires are hanging loosely down the side of the charge. Cut to a two-shot of Carter and Buckles, and the wire is wrapped close to the charge, and Carter starts fumbling with the wire. The wire appears to be a twisted pair of wires - one black, one white. Cut to a view from Carter's right showing Carter and Buckles, and Newkirk coming toward them, and the wire is hanging loosely and untwisted again - as it was during the reaction shot.
The paint scheme of the model of the battleship Bismarck was not the one that the actual ship had. The one shown on the model was a two-tone blue camouflage scheme. In actuality, Bismarck wore a near solid medium gray scheme, with light gray on the bow and stern with a white bow wave.
When the gang is placing the explosives on the bridge, there is a big tree in the background. It is growing so close to the tracks that it would obscure the view of the bridge by any train approaching the bridge, and would have been removed long before this point.
During the 'birthday party', when Buckles and Schultz are holding the model ship (before it breaks), the crack in the hull where it breaks apart is visible.
When the bridge explodes, at the left end of the bridge, it is obvious that the train tracks just end at the bridge. This shows that the bridge is just a prop for the show.
The model of the Bismarck was a plastic model put out by the Lindburg company in the early 1960s. When it breaks, it is obviously a plastic model.
In Klink's quarters, Klink and Hogan are discussing Klink's possible part as the Kommandant. When Klink says, "... I would consent to play the part," his monocle reflects a full view of a stage light.
At the end of the discussion about who will play the Kommandant in the movie, Hogan and Buckles decide on Schultz. Klink sits down dejectedly, Hogan says, "Well, that's show business," and the camera zooms in on Klink. As it zooms in, just before the fade-out, the camera shadow can be seen in the bottom right corner - on the bottom of the brown trim where the curtain is hanging.
When Schultz is in the Kommandant's uniform and wearing a monocle, there is a production light reflecting in the monocle.
During the birthday party, 'Commandant' Schultz is giving a model of the battleship Bismarck. The Bismarck was sunk by the Royal Navy before the US entered the war, so it is unlikely it would have been referred to as 'unsinkable'. Her sister ship, Tirpitz, was still afloat (assuming that it was before Nov. 1944), so the model could have been a representation of that vessel. The painted camouflage on the model was not the correct one.