Continuity mistake: When the three small boys run up and salute Patton, the middle boy stops with the other two slightly behind him to each side, and is the first to salute. When the camera angle changes to view them from in front, the middle boy is instantly behind the other two, and is the last to salute.
Continuity mistake: When the Germans attack during the discussion about air support, Patton's office gets shot up. In one shot we see bullets strafe a wall with a vase in front of it - the vase wobbles but remains intact. Then we see another shot of the same wall/vase combo being strafed - you can see marks on the wall where the bullet impacts are about to be, and this time the vase shatters too.
Continuity mistake: When the two Jeeps arrive at the Kasserine Pass to survey the results of the battle, the second Jeep comes to stop just short of running over a dead soldier. At the end of the scene, the same Jeep drives away, going forward as if to run over that body, but the body has vanished.