Hogan's not wearing his tie leaving the barrack on his way to the restaurant, at the restaurant he's wearing it.
When Kinchloe taped the envelope to Carter's back, he used three long pieces of tape across the envelope. When Hogan rips the envelope off Carter's back, it has one large rectangular piece of tape that barely covers the envelope. There should have been three long pieces of tape hanging from each side of the envelope.
Schultz comes into the barracks just after the secret maps are taped to Carter's back. Just before Schultz leaves, the view is of Schultz, Carter, and Hogan, as viewed from Hogan's left side. Schultz is standing at the corner of the bunk beds, Carter is a couple of feet from the corner of the bunk beds, and Hogan is to Carter's left. As Schultz opens the door, the view cuts to Carter and Hogan, as viewed now from Carter's right - except Carter is now standing at the corner of the bunk beds so he can scratch his back.
There are heavy shadows of Hogan, Newkirk, and LeBeau on the wall at the time just before the recordings are made. These are from the production lights. There is also a large shadow from the thermostat on the wall from the production lights.
Newkirk mentions Speedy Gonzales. Speedy didn't make his debut until the mid-fifties.
The round thermostat on the wall appears to be a 1960s type. Some of the books on the bookshelf behind Hogan as he is speaking into the microphone appear to be from the 1950s and early 1960s.
In one scene, the mirror behind Klink's desk is reflecting something that is not the back of Klink's head, possibly a production light.
When Hogan finishes his interview, the view cuts to a close-up of Newkirk at the microphone. The camera's shadow is on his right elbow. As the camera pulls back, the shadow moves away.
Once again the heroes need a place to hide important documents. They choose to tape them to Carter's back, rather than just storing them in the extensive tunnel network which already contains a barber shop, tailor, counterfeit-money printing press, and shortwave radio set, among other things.
Carter is not married. Yet, on a couple of occasions in the barracks, he is seen wearing a wedding ring.