Near the beginning of the film Pvt. Ferol, when asked by Gen. Mireau, states that he has no wife--but while walking to the firing squad he is crying on the shoulder of the priest that he will never see his wife again.
As Col. Dax is running through the trenches after Gen. Mireau gives his order, a "dead" soldier blinks.
When preparing the three defendants for trial, Col. Dax tells them that he's seen the room where they'll be tried, and that the afternoon sun will be in their faces. In fact, the sun is at their backs.
At the end of the film, when the German girl sings, there are modern (1950s) metal music stands on the stage.
Just before the German girl sings, the soldiers begin to cheer and whistle enthusiastically. In Europe, unlike in the US, whistling is a way of showing displeasure, like booing.
The French soldiers are shown using a British Vickers machine gun in one of the trench scenes. They should have been using a Hotchkiss weapon, or some other firearm of French design.
During the first tracking with Dax in the trenches, the shadow of a boom mike is visible.
During the execution itself the sky repeatedly shifts between gray and overcast in some shots to bright sunshine in others, noticeably changing the natural light, causing shadows and sun glare to appear and disappear from shot to shot.
Camera wire visible in few shots where the prisoners are being taken to their execution spot.
The priest says "et spiritui sancti" instead of the correct "et spiritus sancti".
After the court martial, as the sergeant is addressing the guards describing the procedure and discipline required of the firing squad, all of the guards in the rank have a "710" regiment number collar pin whereas the sergeant (and those in Col. Dax's regiment) have a "701". Although it might be a simple matter of the costuming department transposing the two numerals, the difference might also be intentional. If a firing squad is going to execute three men in a given regiment, then you'd want to have men from another regiment come in and do it to avoid having men shooting their friends.
As Col. Dax walks past soldiers right before the attack, the same soldier with a pipe appears more than once.
After Gen. Mireau slaps the soldier in the trench, he continues on to Col. Dax's dugout and three soldiers carrying a machine gun pass him. The same three soldiers still with the machine gun pass him again when he and Dax are looking at the Ant Hill through the binoculars.