When Cosmo drives Victor's ice truck up on the curb, the back panels fall of before they crash through the window. As the drive away, the wood panels are still on the truck.
In the opening scene, Stallone mentions that they have to jump across 10 roof tops to win the $5 prize that is on the tenth rooftop. During the opening credits, Stallone jumps exactly 14 times to reach the final rooftop.
Although set during the 1940's many of the characters in the film have modern 1970's hair styles, facial hair, and clothing which is not accurate for the time. Sylvester Stallone later corrected these mistakes when he made the film "F.I.S.T." which had the correct clothing/hairstyles.
When Cosmo talks with Annie for the first time on the street, a 1970s station wagon passes by in the background.
When Cosmo and Vic are walking down the street talking about kicking the can, a 1970's truck drives out in the background.