Other mistake: In the final battle where the two rangers are waiting for Upham to bring them 30cal ammo, they fire their rifles through a hole in the wall. At one point two German soldiers are seen dying from the same shot, even though they are at least five meters (about sixteen feet) apart.
Other mistake: When the squad is walking in the field with Mellish singing, they see a halftrack and take cover. Once the halftrack gets shot at by the bazooka, Miller moves to the side of the halftrack shooting the fleeing soldiers. After that, he reloads his Thompson. Then, at the beginning of the last battle, Miller reloads his Thompson for the second time. There is no explanation why he would throw away what is considered a perfectly good cartridge.
Other mistake: When attacking the Tiger, they lift the hatch to throw in hand grenades. This hatch is actually the top of an oil drum. (02:17:00)
Other mistake: When Melish is stabbed by the German soldier, Melish's body isn't consistent with the floor. It's almost as if he his lying underneath the floor.
Other mistake: Private Mellish and another fellow Airborne soldier are manning the .30 cal belt fed machine-gun, and they're quickly running out of ammunition. Private Upham is the ammo bearer, he's supposed to be "Johnny on the spot" with the ammo. After Mellish displaces and sets up a new field of fire he tells Upham to get more .30 cal and to tell the Captain the flank's going to collapse. As Upham is dodging German gunfire he runs by a wall covered with fresh red blood spray. Nobody from that crew was shot yet. (02:15:29 - 02:17:00)
Other mistake: In the final battle scene, soldiers jump on top of a German tank and throw a few grenades in. While the sound of the grenade's fragments bouncing around the tank can be heard, there is no sign of the actual explosion.
Other mistake: When Ryan and Miller are using the mortars without the tube, there is one shot of a German soldier being hit and falling forward. A couple of seconds later this same shot is used again. (02:21:30)
Chosen answer: There's no tree cover to the left. Whoever goes that way will likely be spotted and targeted before the others and get gunned down, but it's their best chance that one of them will make it into grenade range of the nest before they're all killed. It's not a job anyone sane would volunteer for, and the Captain is trying to get someone to volunteer so he doesn't have to potentially order TWO men to their deaths on a mission that all of them, including him, think isn't worthwhile.
Captain Defenestrator