Factual error: A very common error in First World War films. British soldiers were not permitted to shave their upper lips until 1916 - in 1914 almost all (unless physically unable to grow them) would have had moustaches.
Factual error: It is highly unlikely that a Roman Catholic priest would have been permitted to join the army as an ordinary private. He would have been commissioned as a chaplain.
Factual error: There appear to be no NCOs whatsoever in any of three platoons shown, British, French or German. Only an officer each and privates. No sergeants or corporals.
Factual error: Units in trenches were very closely packed and officers visited their subordinates regularly. It is inconceivable that three platoons from different sides could have fraternised for so long without a single more senior officer showing up to find out what was going on. The basic unit was the company and all the officers of the company usually shared the same dugout.
Factual error: In the scene right after the couple sings, they mention that they first met five years ago, in Oslo, Norway. However the city had been known as Christiania since 1624, and was only changed to Oslo in 1924, after the time period of this movie. (00:40:00)