Factual error: The main character is being wooed by Lockheed - an aircraft company, whose representative then gives him gifts for his kids - one of which is a desk model of an aircraft, however it is of an aircraft produced by one of Lockheed's competitors - Grumman, which would be akin to a GM rep giving a toy Ford Mustang as a gift. Both companies continue to remain competitors as Lockheed-Martin and Northrop-Grumman since the government vetoed a proposed merger back in 1998, and at no time have the two companies collaborated on a major project.
Factual error: The opening credits for Lazy Ol' Moon show a copyright of 1951, and says it is in VistaVision. VistaVision was not introduced until 1954.
Plot hole: When Eddie Mannix first views scenes from the movie Hail Ceasar there is a scene depicting Saul of Tarsus (St Paul), but the movie-in-movie's climatic scene and speech are set at the crucifixion of Jesus which happened several years before the events depicted as happening to Saul / Paul.
Factual error: This movie is set in 1951. In one scene, Eddy Arnold's 1955 version of "The Cattle Call" is playing on a car radio. In addition, his name is misspelled "Eddie" in the closing credits.