When Marlene left Klink's office she was wearing a pink suit, black stole and no hat. When she got outside a minute later she was wearing a light purple suit with a black and white striped stole and a matching hat.
After Corporal LeBeau's bogus escape attempt, Colonel Klink states he will transfer him to Stalag 4. He states Stalag 4 is located in France some forty miles from Paris. The actual Stalag Luft IV was located in Tychowo, Poland.
Klink changes his mind and decides to send LeBeau to Stalag 14, Colditz Castle. Colditz Castle was for prisoners who were officers and was known as Oflag IV-C.
When Schultz is talking to Klink from the cooler, he is talking into the side of the telephone, not the microphone. Klink would most likely never have heard what Schultz was saying (at least not clearly).
When Von Heffernick's driver walks around the car to see the scratch on the car door, the close up of the front of the car shows that the car is a Rolls Royce (winged hood ornament and Rolls Royce logo). Even if the car was a spoil of war, it is unlikely that a German officer would drive an iconic British car during the war.
The Count's car pulls away, the observant viewer will see an arm holding a camera to the left, and a person in a shirt to the right of the camera.
The ending has temporal problems. Marlene wants to leave right away, but the Count tells her that they will leave tomorrow, and that she doesn't want to leave on her wedding night. She goes to telephone her mother. Then, when she goes to get in the car to leave, she is in a different outfit entirely, indicating that it might be the next day (and that she and the Count are officially married). Hogan refers to her as Countess, which would also lend credence to it being the day after the wedding. When the car drives off with Marlene and the Count, there is a 'Just Married' sign on back, also indicating it might be after the wedding. However, when Hogan is talking with Marlene, she refers to Klink kissing her for the first time today, so it must be the same day. And, when Hilda announces that the General's car is coming in, she is in the same black sweater and black-and-white checkered skirt as when Marlene first came in. Klink is re-tying his tie, and there are liquor bottles on Klink's desk - used to make Marlene think he is a drunk. These all lean toward it being the same day. There is no way of determining the true timeline.
In the scenes in Klink's office, production lights are reflecting off of Klink's monocle in several instances.
In Klink's quarters, the reflection is particularly noticeable when Klink turns to the camera and says, "You're not going to blackmail me, Hogan."
In Klink's quarters, the reflection is particularly noticeable when Klink turns to the camera and says, "You're not going to blackmail me, Hogan."
The radios got out the gate in the Count's car, but it is never revealed if they actually got to the Underground or not. This is the ultimate destination of the radios. Update: The radios are destined for the underground group in Paris. The Count and Marlene are going to Paris. The car is marked with the 'Just Married' sign. The implication is that, since Kinchloe notified the underground in Paris that the radios will be in a limousine with a 'Just Married' sign on back, the underground group in Paris will see the car coming in and extract the radios while the Count and Marlene are enjoying their honeymoon in Paris.