The window in Lieutenant Gilmore's office door initially displays "Lieut. Gilmore"; When Stu leaves Gilmore's office, the door's window displays "Lt. Roy Gilmore".
When Stu is asked whether he has ever seen the TV show Checkmate (1960), he answers that he watches television only on Friday, the day that "77 Sunset Strip" aired. Checkmate (1960) aired on Wednesdays on a different network (CBS); this episode aired in 1963, and Checkmate (1960) went off the air in 1962, so there would be no way for Stu to have seen "Checkmate".
Grandma's "home movies" are obviously clips from old Warner Bros. feature films. No actual home movies would be staged and edited so professionally.