Hotel Dick - S2-E3
Revealing mistake: Right at the beginning of the episode as the camera pans over to the doors of the movie theater you can see the actors playing the Solomons waiting for their cue to come bursting out of the doors as if they were running out of the theater.
Proud Dick - S2-E13
Revealing mistake: When Harry lands in the yard, you can tell he lands on a crash mat, as the grass beneath him shuffles. (00:01:15)
Chosen answer: Officer Don ended up appearing in 100 of 139 episodes, but I would say season 3 is when he become permanent as Wayne Knight's name appears in the opening credits. However, as he did appear throughout season 2 (first appearance S01E17), it's possible they already considered him permanent at that time since season 3's opening credits also included Simbi Khali (Nina) and Elmarie Wendel (Ms. Dubcek).
Bishop73