Revealing mistake: When we see the new recruits at boot camp, they are wearing M1 Helmets. But if you look closely, they have rivets through the sides of each helmet where the chinstrap bales would be. In reality, the M1 helmet chinstrap bales were and continued to be welded onto the shell of the helmet. This indicates the helmets in the film are probably plastic replicas with the bales being riveted in place.

Captain America: The First Avenger (2011)
1 revealing mistake - chronological order
Directed by: Joe Johnston
Starring: Samuel L. Jackson, Chris Evans, Hugo Weaving, Dominic Cooper
Factual error: When the action moves to England after the failed award ceremony, the British Union Flag hanging from the wall is upside down. The broad white band should be at the top left (nearest the top of the flag pole).
US Army soldier: Wait! You know what you're doing?
Steve Rogers: Yeah, I've knocked out Adolf Hitler over 200 times.
Trivia: Some of the members of Captain America's wartime elite squad are taken from Marvel Comics WWII based "Sgt Nick Fury and the Howling Commandos" - such as Dum Dum Duggan and Gabe Jones.
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Answer: It's a drinking song from 1883 called "There's a Tavern in the Town."
LorgSkyegon