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.
Answer: Most likely Mr Warbucks had some sway in the outcome of things. Because Mrs Hanngan in the end did try to save her life, and was also assaulted by her own brother when she turned on him, Annie and Mr Warbucks statement probably got the police to let her go. Also it would seem that Punjab liked her. She came around to the right side in the end.