Al's arm can be briefly seen reflected in the dressing room mirror. Since he is a hologram, he shouldn't have a reflection.
On October 7, 1957, Sam says that the Soviet Union launched Sputnik two days earlier. In actuality, it was launched on October 4, 1957.
This episode claims to take place in St.Louis, Missouri. When Sam drives through the neighbourhoods to visit Moe Stein's home, palm trees are visible in the background. No such trees can be found in St.Louis.