Plot hole: Sally Rogers appears on the Stevie Parsons show which is a late night talk show, the next morning she receives letters from as far away as Hawaii... the US mail isn't that fast.
The Great Petrie Fortune - S5-E6
Plot hole: If Rob was just 12 or 13 when he last saw his grandfather (that's what they said in this episode, also he never called his grandfather ever from what it looks like) then his grandfather wouldn't know that he has been working on a TV program. (He started working on the Alan Brady show when he was 20, not before).
Suggested correction: First of all, it is Rob's great-uncle, not his grandfather. And what makes you think he wouldn't know? Off the top of my head, I can think of a dozen ways he could have known. He was watching the show and saw Rob's name in the credits. His brother called him to brag about his grandson. He read a magazine article about television comedy writers. Etc. Etc.