When Gaetano falls because of the slippery ice, his hat remains in the street. In the next instant, In the following scene (from a new frame), he has his hat on.
When Gaetano kills the busboy, the shot throws his victim ten feet clear across the room. Gunshots cannot do that, as was proven conclusively on Mythbusters.
Per opening credits, events in this episode took place in 1950. The song played in the nightclub scene, Moanin' by Bobby Timmons, was written and first recorded in 1958 when Bobby Timmons was a member of Art Blakey's Jazz Messengers.
As Gaetano is crossing the street before slipping on the ice, modern (rather than period-correct) route marker signs for U.S. 12 and U.S. 20 are visible in the background. Neither U.S. 12 nor U.S. 20 pass through the Kansas City area. The combined U.S. 12-20 does however pass through the south side of Chicago, as well as the towns of Oak Lawn and Evergreen Park, Illinois.