The amount of papers in Penny's hand after being given the script suggestions and when she talks to Junior then the writers.
At the end of the film the camera pans up to the top of the building, showing the damaged WBN logo. However, the holes where the letters came out of the wall are missing.
When Penny and Roger are first arguing, they go through swinging doors onto the stage. When the cut is made, in the middle of the conversation, they are suddenly in the middle of the stage and the doors are nowhere to be seen.
when Roger dressed as a penguin gives billy the envelope for penny it's yellow and large, yet when billy delivers the letter to penny its a smaller white envelope.
The portrait in Gen. Whalen's office shows the general wearing a service dress green uniform which was not adopted by the U.S. Army until the mid-1950s. In 1939, when the movie is set, the general would have worn a khaki uniform.
Roger refers to the cops as a bunch of Nimrods because they were acting stupidly.
The word Nimrod comes from the Bible and is named for a great hunter. Bugs Bunny used the term Nimrod to mean hunter when talking about Elmer Fudd in a 1940 cartoon, one year after this supposedly takes place. It would not be a euphemism for stupid for many more years.