Continuity mistake: When Mr. Warbucks is talking to Miss Hannigan, he mentions adopting Annie. After the camera angle changes to see her reaction, the folded blue paperwork suddenly appears.
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.
Continuity mistake: When the autocopter lands for Punjab, the pilot has a boom mike. A moment later, it's gone.
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.
Continuity mistake: When Rooster is in the hallway close to the railing, notice the colour 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.
Continuity mistake: Pepper confronts Molly and Annie comes to comfort Molly. Pepper lies down while Annie sings and her arm's position differs between shots.
Answer: Mrs. Hannigan's box of Annie's parents' things might have the only record of her birth certificate. This is the 1930s, after all. Paper records went missing all the time.
Captain Defenestrator