(at around 4 mins) While running down the top flight of stairs to play with the neighbor boys, Tommy's breath is visible. His breath is visible again (at around 25 mins) while he is running to the police station, just after he runs past the canopy of 136th. This is due to shooting in the late Fall when the movie is set in the 94 degree heat of summer.
When Tommy is running away from the couple in the abandoned part of the building, he accidentally finds the sailor's body. When he does this, the sailor's legs move.
In the confrontation between Joe Kellerson (Paul Stewart) and Tommy (Bobby Driscoll) in the apartment, the closeups are out of focus but were never reshot.
(at around 1h 8 mins) When Tommy pushes one end of a long roof beam off the beam segment on which he is perched, the free end of the beam falls, but its other end stays attached to the wall, so it briefly hangs down along the wall. When the top end breaks free from the wall, the cables can be seen attached to that end that were used to pull it free.
When Tommy's father returns home unexpectedly and locks him in his bedroom and nails the window shut he does not appear to notice the note Tommy left on the kitchen table. Yet when he returns later to the apartment and finds Tommy has gone missing he then sees the note.