Joe E. Brown and Martha Raye were (separately) both known for their wide mouths, so I guess it was inevitable that someone would decide to team them on screen. Unfortunately, this movie isn't very funny. The cleverest thing about this movie is Joe E.'s character's name: he plays a ham actor christened Marlowe Mansfield Booth, which is the name of a 16th-century playwright and two 19th-century actor/managers.
Joe E. inherits a college (don'tcha hate it when that happens?). This is an American movie, so of course the 'college' is merely a front for a football team. (Classes? What classes?) Inevitably, everything Joe E. and Martha need to accomplish depends on their team winning the Big Game. Inevitably, Joe E. goes into the game at the last moment. So far, so good: Joe E. Brown was an extremely athletic man who often played inept weaklings on screen, and several of his films relied upon his character suddenly developing athletic prowess at the climax. Unfortunately, in this movie Joe's success is more down to dumb luck than anything else. The number on Joe's football jersey is 13 ... which tells you how obvious everything in this movie is.
I have mixed feelings about Martha Raye. I consistently find her unfunny, and I dislike the characters she played. In 'Monsieur Verdoux', I kept hoping that Chaplin's attempts to murder her would succeed, and I was annoyed that she survived at the end. However, in the real world, Martha Raye risked her life to perform for American servicemen in combat zones during several wars, and she was a tireless advocate on behalf of Vietnam veterans. In the last years of her life, Martha Raye hoped to get a film made based on her experiences performing in the USO during World War Two. Unfortunately, a certain well-known 'actress' ripped off the facts of Martha's life and made a flop movie that put paid to any chances of a straightforward Martha Raye biopic. So, I have a lot of sympathy for Martha Raye as a person even while I intensely dislike her as a performer.
And she's extremely unfunny in this movie. Several reliable character actors are in '$1,000 a Touchdown' - Eric Blore, Tom Dugan, Matt McHugh, Jimmy Conlin - but none of them have any decent material. All of them have been funny elsewhere, but none are funny in this movie. I was grateful for the presence of tall shapely brunette Joyce Mathews as a campus vamp. I'll rate '$1,000 a Touchdown' 2 points out of 10.