Visible crew/equipment: When Punjab is remarkably "flying" the toy plane by using his mind and interesting hand movements, when it shows a close up of the floating plane, you can see the string to which it is attached.
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.
Continuity mistake: In the scene where Rooster, Lily, and Ms. Hannigan are singing "Easy Street" and dancing on the stairs, Ms. Hannigan's foot goes into the wall creating a hole, but that hole is no longer visible in following shots. Also, you can see the outline in the wall where her foot is suppose to go.
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.
Continuity mistake: When Rooster is in the hallway close to the railing, notice the color of his shirt and suspenders. Then notice when he leaps on top of the railing and is spinning around, all the sudden his shirt color is different and you cannot see his face, but when he is done spinning the shirt color is the same as first seen.
Audio problem: On the bridge, sounds of a nearby boat can be heard; however, a boat is never actually seen nearby, nor any lights on the water.
Audio problem: When Ms. Hannigan is singing "little girls", the sounds that the two bottles that she clinks make a glass-against-glass sound; however, the bottle that she dumps into the bathtub floats in the water like plastic instead of sinking like glass would.
Continuity mistake: During the final scene, Annie and Daddy Warbucks are watching a huge fireworks display. Dozens of fireworks are going off simultaneously and all the bursts are either blue or pink. In the close-up shots of Annie and Daddy Warbucks, only an occasional flash of light illuminates them and it is always orange.
Factual error: If Annie was dropped off at the orphanage as a baby and they aren't supposed to have any fun and really don't have any toys or anything, where does she learn how to swim? This is during the depression era. I'm pretty sure these were no community pools. She jumps into Mr. Warbucks' pool the day after she arrives and starts doing a backstroke.
Audio problem: When Miss Hannigan, Rooster and Lilly are singing the song "Easy Street" Rooster encourages his sister by saying "Hit it, Sis." But he actually says "Hit it, Carol." The "Sis" is an overdub. This may not be a subtitled line but is clearly spoken.
Other mistake: When Miss Farrell and Mr Warbucks are looking for Annie, Punjab tells Miss Farrell which bridge Annie is at, but when Miss Farrell relays the info, she only says "They're on the bridge", and yet Mr Warbucks says "I know, I know" as if he KNEW which bridge she was talking about.
Visible crew/equipment: In the rescue scene with Annie and Punjab on the bridge, when Annie is climbing the ladder, in the wide shot you can see it's not a girl but the stunt double, quite possibly a small man.