Revealing mistake: When Schultz is talking to Hogan and Le Beau, the guard outside walks past. As he does, you can see three shadows from him revealing the studio lighting, rather than him really being outside.
Continuity mistake: Hogan takes the movie camera from Klink right side up. The next second, it's upside down. Then when Hogan goes to dunk the camera in the water, the lenses are pointing to his right. In the close up, they're facing his left.
When Klink is begging Hogan to trade places with him for fear of assassination, he says to him something like."I want to live til 80...all my family has lived til 80." Werner Klemperer, who played Klink, passed away in 2000 aged 80.