When Dick and Tess are in the diner with The Kid, the boy finishes a glass of milk and then runs for the door. Tracy puts him back in his seat, during which time the glass has refilled itself.
The credits, in order of appearance, show Pruneface then Mumbles; Mumbles first appeared long before Pruneface did.
When Tess finds Dick Tracy and Breathless kissing, she is carrying two ice creams. Both with a round top scoop. In the next shot of Tess, one is licked flat. In all shots following, the ice creams are either melting, not melting, etc., but never exactly the same twice.
When Dick Tracy fills the cup of water, it is filled to the brim, but when he waves the cup in front of Mumbles it isn't quite full.
When Big Boy has Mumbles wipe the cement off of his shoe, he's facing Breathless. Then the camera gets a closeup of Big Big stepping away while Mumbles is wiping his shoe off. When camera changes again, Big Boy never stepped away. He's still facing Breathless.
When Dick Tracy jumps off the seesaw and through the ceiling window, he lands on the roof. This clearly shows the face of the stuntman doing the jump back down and then looking around before running off.
In the final major shootout, Dick Tracy and the other cops obviously fires more rounds than is available from a standard drum (they do not reload on-screen).
The yellow Hudson is a 1940 model. All other vehicles are mid-30s.
When Tracy is fighting the man in the shack, he says several lines but his lips clearly do not match the dialog.
When Big Boy and Flattop enters the vault, the latter says "It's Tracy's dame".
His lips do not move when this line is spoken.
A little platform is mounted on the back of the car for the kid to climb on.
When Dick Tracy jumps out of a window and slides down the lamp post, he bangs his head on the curve of the pole towards the top. (This was Beatty doing his own stunt.)
Towards the end, Tracy says that kidnapping is a federal offense. This is inaccurate. To be classified as a federal offense, a crime must meet at least one of three different criteria: it must violate US federal legislation, occur on US federal property, or occur within Washington, DC.