The nut filled closet was first done on the Dick Van Dyke show on 6 February 1963. It was Season 2, Episode 20 of that show. When it was done on The Dick Van Dyke Show, Mary Tyler Moore opened the door of her closet and was bowled over by the same kind of flood of walnuts.
Due to the series ending after the next episode, this was the last appearance of Mrs. Brown, (Pamela Britton), and Detective Brennan, (Alan Hewitt).
The title is a reference to the Bible's 23rd Psalm: "My cup runneth over."
The name Red Squirrelton, very appropriate for a squirrel who became human, is also probably a reference to popular tv star Red Skelton, whose show was also on CBS
At about 58 seconds into this episode, Ray Walston breaks character. Using one of his inventions, he changes a glass into a jar of aspirin. He picks it up and briefly laughs and says "...it should have been a lamp shade." Guess they didn't want to re-film that scene.