One of the production drawings for "Ben-Hur" in Saul's office is missing after the first scene.
The top button of Guy's blue shirt is buttoned and unbuttoned in alternate shots.
The wall telephone (in Guy's apartment), is not period. They didn't have phones like that until the late 60's. The phone cord is not accurate either. That phone appears to have a modular connection, and not the thick type cord in the older phones.
The sign on the Post Office says United States Postal Service. The USPS didn't exist in the 1950s. At that time it was the United States Post Office.