The Variety cover announcing Lonesome Rhodes on-air meltdown not only mis-spells his last name as "Roads" but is also dated "November 21, 1956" which is well before the other dates in the movie, for example, earlier he was picking Miss Arkansas Twirler 1957.
When Lonesome Rhodes is critiquing Senator Worthington Fuller's presentation style, the camera angle switches several times. From the front, his left arm/hand is pointed towards the ceiling; however, the reverse angle shows his left arm lowered and pointed to the side.
In the scene where Marcia is recording Larry in the jail, she surreptitiously records him as he is warming up. When he announces that he's ready, she reveals the microphone and then stops the tape. However, when she is replaying the tape, Larry can be heard asking if she had the recorder on the whole time.
In the protest scene outside of the mattress store, protesters set fire in a trash barrel that has the letters D.S.N.Y., presumably for "Department of Sanitation of New York". However, this scene is set in Memphis.
When the Sheriff escorts Marcia into the jail holding cell, he welcomes her to the "Tomahawk County Jail". However, in the exterior shot just prior the cornerstone of the building plainly reads "Clay Co." That's because the exterior was shot at the Clay County Courthouse in Piggott, Arkansas. There is no Tomahawk County in Arkansas.
"Lonesome Rhodes" is in jail for a week for being drunk and disorderly. When he's asked to sing a song, he pulls his guitar out of his case, along with a visible bottle of whiskey. It's highly unlikely the police wouldn't have searched his guitar case as a matter of safety (he could have had a gun in there); certainly, they would have found AND CONFISCATED a bottle of "hooch," especially to a prisoner who was charged with drunkenness in the first place.