गूफ़

In the opening scene after Sgt. Rasmussen takes a flag from a German soldier, he has nothing in his hands when he's yelling at another soldier; in the next shot, the flag is back in his hand.

They are mainly clearing Anti-Tank mines, and indeed mention this in the dialogue. However, Anti-Tank mines are designed to not be triggered by a person's weight, so troops can cross them without them going off--so that they are still in place and active when armored vehicles in support of the troops ultimately cross the same path as the troops. Anti-Tank mines need several tons of pressure to activate. In the film, they are treated like eggshells.

The boys always have 'fresh' haircuts throughout a film that covers three months. It's unlikely that they had a barber at hand, or even a pair of scissors.