Plot hole: The letter that had to be delivered to the Colonel should have been completely ruined when the Corporal was in the river.
Character mistake: Scene where they push the truck out of the mud; right after they drive away in the background you can see that the other side is flat grass. They never had to do all that.
Suggested correction: Trucks of that era were not equipped with limited slip, nor posi-traction differentials, so having their truck land in mud on the drive axle side of the differential resulted in exactly what's portrayed in the movie.
Factual error: While crossing No Man's Land an abandoned tank is seen. Tanks were not used on this battlefield until April 9th, 3 days later than the date the film is set. (00:20:10)