Plot hole: In the very last episode of the show, "George Decides To Sta-Local Where It's Familiar", Angie mentions that they conceived their "kids" there, referring to both Carmen and Max. However, the season four episode "George Takes a Stroll Down Memory Pain" showed flashbacks where Angie and George were living with Benny, and Angie was far along in her pregnancy with Carmen. Only Max could have been conceived in the house that they are currently living in. I want to add that in the episode 'Valentine Massacre', George says"What about the first time we made love. What were the odds in Vegas!?!"
Continuity mistake: In some of the beginning episodes, whenever George is at work, you can notice that it was originally called "Powers and Sons Aviation", but later in the show it calls them "Powers Bros. Aviation." We even see the Powers Bros. in a few episodes, and in one episode Mel Powers' son smashes up the factory.
Continuity mistake: Max gives Angie a charm bracelet for Valentine's Day with her birthstone, garnet, in it. Garnet is the birthstone for the month of January. Episodes later, George mentions that Angie's birthday was in the summertime because when she was angry with him, there was still light out during dinner.
Answer: His last appearance was in the episode "God Needles George. He had a tumor in that episode, but in the end was better, and that was the last appearance of him on the show. He was occasionally mentioned afterward, so it is assumed that they still had the dog for the rest of the series.