The order of the verses of "Silent Night", as they are performed in the movie, are not quite correct. After the first verse in the movie they sang the last and then the second.
The poem that was the base for "Silent Night" was written in 1816 in Mariapfarr, before Joseph Mohr came to Oberndorf and received Gruber's melody only in December 1818. In the movie Mohr writes the lyrics in 1818 and asks Gruber the very next day to write the Melody for it.
Joseph Mohr and Franz Xaver Gruber didn't meet until Mohr started his Duty at the church in Oberndorf in 1817. In the movie they knew each other already before that.
During the Midnight Mass on the 24th December 1818 Priest Joseph Mohr was playing the guitar when singing "Silent Night". In the movie composer Franz Xaver Gruber was playing it.
The first masses composed by Franz Xaver Gruber were not performed until the early 1830s, while in the movie one of his masses is performed in 1813.
In the pub scene in 1818 a man mentioned that Laufen remains Bavarian and Oberndorf/Rupertiwinkel is part of Salzburg. This refers to the Contract of Munich, which however was made in 1816, 2 years before the scene's setting.