The photograph of Captain Gannon's wife behind his desk is the same photograph as Colonel Potter's wife in M*A*S*H (1972). Both parts were played by Harry Morgan.
The famous catchphrase "Just the facts ma'am" was never actually said by Jack Webb/Joe Friday, but by comedian Stan Freberg.
Detective Streebek's television watch was real. SEIKO invented it in 1983. It had a black-and-white display and a separate battery pack/tuner about the size of a Walkman.
When Joe Friday first sits down at his desk, a pack of Chesterfield cigarettes is on top of the newspaper. Chesterfield sponsored the Dragnet radio series and Jack Webb, the original Joe Friday, used to participate in Chesterfield ads during Dragnet radio and television episodes. Another cigarette brand, Fatima, was the original sponsor of the Dragnet radio series.
Joe Friday quotes the dress code to Pep at the beginning of the film pretty accurately.