When either Nikolaus sings alone, or in a duet with his love Anna, it's very obvious he is not singing himself. The singing voice is clearly different from his spoken voice, and the song's words don't match with the lips (for both Nikolaus and Anna) on several occasions.
Before exiting their trench, the French lieutenant calls for fixing bayonets. Which every soldier does as can be seen. However, when fighting in the German trench, no bayonets can be seen anymore on the rifles.
When Anna and Nikolaus are kissing in the scene before they make love, in a close up shot their lips are almost touching, and in the next shot their heads are next to each other cheek to cheek, and they're hugging.
In the film the musical exchange is prompted by the Scottish troops: in reality, most incidents began with the German troops singing carols from their trenches (but not exposing themselves to the enemy - both sides remained in their trenches) with the opposing troops countering with carols of their own. The film was advertised as "based on a true story", but neither the marketing nor anything in the film claims it to be a historically accurate account of the events. At the end of the closing credits it states, the story is based on a compilation of various documented events which took place along the front during WW1. Director Christian Carion said in the DVD commentary that he included Scots, rather than English, in the story because he wanted bagpipe music.
Most of the Christmas Truces began as a mutual agreement by both sides to bury their dead. In absolutely no case was there any record of the incident being started by a singer moving out into No Man's Land carry a lit-up Christmas Tree. In many cases where Germans did venture into No Man's Land, they were shot by snipers.
When the three commanders meet and discuss their wives, the French commander says he lost the photo of his wife and shows a sketch. The German commander recognizes the sketch of the woman from a photo that is inside a wallet he found on the battlefield (and subsequently returns the wallet to the French officer). However, in the beginning of the film, the French commander is looking at that photo. In the shot, the photo is of both the commander and his wife. If the German officer can recognize the wife from a sketch, surely he would recognize the French commander when seeing him in person?
Snow around the fresh graves, but not on the graves. When the graves were dug, where did they put the dirt so as not to disturb the surrounding snow? And if it snowed since the graves were dug, why is there no snow on the graves?
When the German soldier is marching toward the enemy holding the Christmas tree, he is singing "Adeste Fideles" - the original Latin song translated into English as "Oh Come All Ye Faithful." For the chorus he is clearly singing "Venite adoramus" - meaning, "Come, we adore". This is wrong. It should be "Venite adoremus" - "Come, let us adore". How could everybody in the cast and crew have missed a mistake like that? The song has been around since the 1600's. The only possible answer: the singing was dubbed in later, in the studio, where it might have been missed. But still... really?