Factual error: The strong current of the river the main character falls into carries him to a considerable waterfall. There is not, nor has there ever been, a river of that kind in Flanders' Fields, let alone a waterfall. Anyone who has any insight into the geography of the region will tell you it is flat as can be. The largest body of water, the Yzer, gently meanders and flows into the Channel, even during really rainy times.
Continuity mistake: The injury Schofield suffers to his neck is healed by the time that he gets to the front line.
Factual error: In one scene you can see the bottom of a soldier's boot, and it has a light blue rubber part on it. They didn't make colored soles back during WWI.
Other mistake: At the start of the trench running scene where the soldiers charge, keep looking at the far left of the screen. You will see a small group of soldiers already running who were not in the trenches. In addition, they seem to be running without weapons.
Factual error: The British medical station is above ground and too close to the front lines. It is well within range of German artillery. Normally, such large open-air stations would be miles behind the front lines. Smaller, underground aid stations would give first aid to the wounded. Then they would move to the larger medical stations.
Continuity mistake: When Schofield drinks milk, he has no bandage on his hand.