Factual error: During the orphans' rendition of "You're Never Fully Dressed Without a Smile" Molly is seen with a plastic drink bottle (that makes a plastic-bottle-esque "thunk" when thrown). The movie takes place in 1933, however polyethylene terephthalate (the kind of plastic used for drink bottles) was not developed until 1941.
Factual error: They take Annie to the movies to see Camille except there's a problem - Annie takes place in 1933 and the version of Camille they're watching (starring Greta Garbo) didn't come out until 1936.
Factual error: Throughout the movie, all the women (with the exception of Miss Hannigan) are shown to be wearing full coverage pantyhose (you can most see this in dance numbers). Pantyhose that covered all of the leg and buttocks were not invented until 1940 (Annie is set in the 30s). Any hosiery worn prior to that would have been stocking type that only came to the top of the knee.
Factual error: This film is supposed to be set in 1933, but at one point we see a helicopter, a machine that wouldn't be invented until after World War II.
Suggested correction: The helicopter was originally theorised by Leonardo da Vinci in the 1400s. Early practical versions began to appear in the 1920s, and by 1932, helicopters were able to carry more than one passenger. Although a machine that could carry three people from NY to D.C. was not possible in 1933, in the context of the movie, Warbucks would be able to afford a privately built copter, with improvements of course, for personal use.