Continuity mistake: During the opening of "This Is the Army" [the stage musical], there is a large choir of men singing the opening number, "Some Dough For The Army Relief": from about the second row back, the men's mouths are moving appropriately for the lyrics they're singing, but much of the front row is singing with these obnoxious cheesy grins, not even bothering with more than the most feeble attempt at proper mouth movement. [This is painfully evident during the line "let him do what we had to do."].
Deliberate mistake: During the early rehearsals for "Yip Yip Yaphank", a group of men are around the piano singing "God Bless America", and we hear the following lyrics: "Stand beside her/And guide her/TO THE RIGHT/With a light from above". This is NOT an error; I'm guessing that those were the actual lyrics of the rough draft, with the capitalized line above changed to the present "Through the night/With a light." at a later date.
Factual error: The opening scene of the film, with a woman singing "For Your Country and My Country" at a bond rally, is supposedly set in 1917, but her hair and clothing are pure 1940's: calf-length skirt and curled shoulder-length hair, neither of which was acceptable attire for a lady in 1917.