The Coat of Arms hanging on Col. Klink's wall in which the microphone is hidden is made from plywood as the layers of the board can clearly be seen on its close-up.
The stock footage of the American cargo planes that drop the "dummy" commandos are, in select spots, painted "International Orange." Tactical airplanes in wartime would not be painted as such.
The stock footage used of transport aircraft dropping paratroopers was of C-119's in Arctic markings. The C-119 entered service in 1949, and the Arctic markings utilized (including very obvious "U.S. Air Force" painted on the noses of the aircraft) were mid- to late-1950's vintage.
When LeBeau comes back from the truck with the snuff box and the fan, he opens the fan and indicates it is made of ivory, and is so old it's yellow. He then closes the fan angrily. If the fan had been that old, being a museum piece, LeBeau would have treated it much more gingerly, lest he cause permanent damage to the fan.
When LeBeau is put into the truck and a German guard comes by, he does not understand English, and has problems with the word 'emergency'. Seconds later, Schultz tells him to leave in English, and the guard leaves, understanding him.