Factual error: In the scene where Bill Murray is listening to "Have Yourself a Merry Little Christmas" the newer, revised lyrics rewritten in 1957 were used. The original lyrics from the original song written in 1944 were deemed too depressing by Frank Sinatra. The lyrics we hear in the movie set during the winter of 1944 were not published until about 13 years later.
Factual error: In the Have Yourself a Merry Little Christmas scene, ignoring the inclusion of the 1957 lyric change, as noted elsewhere, somehow a recording of the song was made and delivered to the Battle of the Bulge pretty quickly. The song was introduced in the film Meet Me in St. Louis on November 22, 1944, the Battle of the Bulge started December 16, 1944 and ended January 25, 1945. Pretty quick work for the times.