Other mistake: During the flashback of the soldiers executing the Dachau guards, the soldiers are in a line opposite the guards who are in a line against a fence. The soldiers all start shooting at the same time, but we are shown the guards being mown down by gunfire in succession, like dominoes, rather than simultaneously.
Other mistake: When Teddy and Chuck are smoking under the portico roof during a downpour, they are first shown from the back and are completely in shadow, from head to toe. The shot changes to the front and their head and shoulders are lit from above. This would have been seen from the back as well as the front if it were intentional.