Revealing mistake: The first shot of the train the view is normal. Then after Lebeau starts in reverse you can see the smoke trail going in the wrong direction. The final shot shows the train moving in reverse, but notice the smoke trail is going to the rear of the train instead of the front as it should be, since it's moving in reverse. (00:15:05 - 00:22:25)
Plot hole: In his German uniform, Col. Hogan wears a number of decorations, among them the Iron Cross first and second class. When did he earn those if he has just been drafted for a suicide mission? After all he was not posing as a Wehrmacht soldier for a change but wore the uniform "officially". (00:17:00)
Answer: The core POWs regularly escaped and returned to the prison camp because they made it their mission to conduct espionage and commit sabotage in the surrounding German territory. They also collaborated with different underground resistance groups and used a network of secret tunnels to help prisoners from other POW camps to escape, who then relayed vital information back to the Allied forces. Hogan and his men maintained the illusion that Stalag 13 had never had any prisoners escape in order to avoid their covert operations being shut down. Being that the prison camp is set in Germany during WWII, there were no American embassies.
Hogan has mentioned to different characters that they are actually stationed at Stalag 13 to help allied soldiers and prisoners from other Stalags to escape Germany.