Rupert is talking to Jerry in Jerry's limousine. Rupert bandages his hand with Jerry's handkerchief. In the next sequence in the car the bandage is missing. Following this Rupert's hand is again bandaged.
When Rupert shows Jerry a picture of his pride and joy he holds it with his index finger over the top, but in the next shot it is his thumb over the top. This is repeated when Rupert then tells Jerry to take the card.
When Rupert and Rita are being kicked out of Jerry's countryside home, while Jerry replies "Not them, me.." the left half of the glass door in front of him is closed, but in the next moment we see Jerry from behind closing it.
The TV sets in the store display window near the end, where Jerry Langford angrily watches the end of Rupert Pupkin's TV appearance, are all tuned to channel 3. There is no TV station in New York City on channel 3 (two major stations, WCBS and WNBC, are on channels 2 and 4 respectively). However, channel 3 was (and is) commonly used for connecting video devices such as home computers and videotape recorders to TV sets. The film crew most likely rigged a videotape player to the TVs to mimic a network broadcast, thus requiring them to be tuned to channel 3--a small detail that most audience members wouldn't have noticed.