Factual error: The guard outside Klink's office and the two Gestapo soldiers guarding the gold truck have MP38/40 and a Thompson submachine gun, but carry rifle ammunition pouches instead of the long ammo pouches that carried the 30-round magazines used by the MP38/40.
Other mistake: After the truck is stopped, Newkirk tosses a dart at the tyre in order to flatten it. Since the tyre hit was the rear tire, there should have been the track from the front tire, but wasn't. Also, a puny, hand-tossed dart couldn't have penetrated the thick construction of a heavy-duty truck tire, let alone flatten it in twenty seconds.
Other mistake: When stopping the truck and Schultz, the area directly behind Carter and LeBeau can be seen to be a matte painting. The reason is because where they are is completely covered in snow, but the open area is very little, and there is a huge snowdrift piled up at the wall.
Factual error: When the men are lined up to take the strongboxes of gold to switch with bricks, each man in line easily hefts and tosses them to the next man. Gold bricks weigh over 27.5 pounds (12.4kg) apiece. If there 10 bricks per box (going by the size of the boxes), then that comes to 275 pounds per box, plus the weight of the box, which these guys are tossing around without a problem.
Continuity mistake: After the POWs cut the stairs outside Col. Klink's office, Sgt. Schultz walks down them. There is a guard standing to his right. After a switch to show the POWs, when the camera goes back to the stairs, Col. Klink walks out and falls when the stairs collapse. The guard is missing without making any motion to move before. When everybody rushes to Col.Klink, the guard runs in from the left also.