OK, there are several minor errors here. One, Capt. Miller is given a Thompson when those were only issued to paratroopers. Two, when Jackson kills the sniper in the bell tower, he removes an American Distinguished Rifleman Medal from the German's chest.
Three, in the final battle scene Ryan and Miller are shown hitting rounds against a box and throwing them.
This is impossible. If this could be done, the round would explode in their hands.