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 Big Boy Caprice has all the mob bosses together, Itchy stands behind him. In a close-up, Itchy scratches his neck with his right hand. But then it cuts back to Big Boy and Itchy has his right hand at his side.
When Dick Tracy jumps of 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.