Factual error: The Map of Europe used for plotting their route displays the Netherlands incorrectly, showing its two major central polders (low-lying reclaimed landmasses surrounded by dikes) which weren't drained and finally completed until 1968.
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: It was incorrectly stated that the Madonna and Child was in the Cathedral at Bruges. It is actually in The Church of Our Lady in Bruges.
Factual error: In the final scene as they turn from the Madonna and Child, they are not exiting from the correct building. This building is neither the incorrectly stated cathedral in Bruges nor the correct home of the sculpture, the Church of Our Lady.
Factual error: In the 1977 flash forward scene, an elderly Frank stokes is seen standing close to the Madonna of Bruges. But the statue has been behind bullet-proof glass and a 15 foot barrier since 1972. (01:55:00)
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.
Factual error: On the facade of the architectural model of the proposed Fuhrer museum, the swastika symbol is displayed horizontally, in a "square" orientation. The Nazi symbol was always displayed in a diagonal orientation ("diamond" shaped, ie. tilted at 45°).
Factual error: Roosevelt is shown receiving a report on all the Monuments Men's activities. However, finding the Madonna at Bruges takes place after the war ended in early May 1945, as the Russians are arriving to take over the areas in eastern Germany occupied by the Russians. President Roosevelt died in April 1945, so President Truman should be receiving the report.