In the early scene where Lenny leaves home, he moves his suitcase from the chair to the floor, then tells his mother that she's going to give herself a heart attack, and when the camera cuts back the suitcase is back in the chair.
In the early scene where Lenny leaves home, he's outside on the sidewalk. It's overcast, and hardly any shadows are seen. Mrs. Tupperman calls down to Lenny from a window above. The view from her window looking down on Lenny shows him clearly bathed in sunlight, casting a shadow. As he replies to her, the camera angle changes back to him at street level, but again he's in overcast, with no shadow.
Set in 1953, but the unmistakable twin towers of the World Trade Center (completed in 1973) are visible in an exterior scene.
Larry's father is always reading newspapers that are clearly props printed on stiffer white paper than cheap pulp newsprint actually in use in 1953.
The bottles of Budweiser in the film are the more modern 1976 vintage and not the correct 1953 bottles.
Barney has long hair and a beard which wasn't in style among men in the early 50's.
Photo of Jayne Mansfield on wall of Twentieth Century Fox casting director in 1953, at least two years before she was signed to studio or even beyond bit player status.
In one scene, Larry's mother, an opera fan, refers to a recording "from Verdi's 'Tosca'". "Tosca" was composed by Puccini, not Verdi.