Deliberate mistake: The German army is using American Sherman tanks, presumably easier to get for filming.
Deliberate mistake: Smith and the team come down the mountain and into the village at dusk, yet it is light out during the entire movie.
Deliberate mistake: After John poured gasoline on/around the Mercedes, set it on fire, and it was surrounded by flames, he was able to put his hand through the flames to open the rear passenger door and get inside. He did not burn his hand on the hot metal door handle and did not catch any of his clothes on fire or even singe his hair. His hand was not injured because he was able to hold and aim his pistol with it. (00:35:04)
Deliberate mistake: In the scene near the end of the movie when Trigger is in the bilge trying to stop the air leak, the concussion of an artillery shell fired from the destroyer shakes some pipes loose. The mistake is that one of the flanges visible on a section of pipe has no bolt holes, making it impossible to join that pipe to anything.
Deliberate mistake: The German tanks in this movie are not really Tiger tanks. They are Russian T-34's made to look like Tigers. The T-34's are done up very realistically, including Zimmerit (the wavy pattern on the hull of the tiger), which was an anti-magnetic paste put on the tank.