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The Other Darrin: Deacon's son, Kirby Palmer, was played by three separate children over the course of the show.
The same goes for Deacon's younger son, Major, who was also played by three children.
To be fair, though, this is the only way a show not structured as Real Time can continue to show young children.
Also, when Spence's mom Veronica first appeared in "S'Aint Valentines", she was played by Twin Peaks star Grace Zabriske (as Anne Meara was playing another role in that episode). By her next appearance, Meara had taken on the role and would play it for the rest of the series run (Anne Meara is Jerry Stiller's Real Life wife, which is played with later on when flirt and date).
Doug's Boss, Supervisor O'Boyle was played by Sam McMurray throughout the entiere series, except for Season 1's "White Collar", where the character was played by John F. O'Donohue. The character's name is given as "Jack" in the credits but McMurray's character's first name is Patrick. While the fact that Doug could have two supervisors with the same last name is not completely impossible, a later episode centered around a flashback to when Doug first started working at IPS (season 8 episode "Consummate Professional") has the McMurray character as Supervisor.
Also Carrie's Boss in Hornstein & Steckler, Mr. Kaplan was played by Victor Raider-Wexler. When Carrie eventualy gets a job at a Real Estate Firm her new boss was played by the same actor.