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.
Character mistake: When Sally asks if Rob would give his party guests malaria, Rob responds later on with, "Oh, Roe, I would never suspect you!" Roe was Rosemarie's nickname on set.
I Do Not Choose to Run - S5-E16
Character mistake: Rob tells his council men that "Richie loves helping his mom in the kitchen" yet every time she's in the kitchen cooking or doing anything of the sort. Richie is nowhere to be seen. The only times Richie is near the counter is when he's hiding under the counter, or drying his hands like the rest of the family.
I Do Not Choose to Run - S5-E16
Factual error: When Rob tells the name of the street he lives on in this episode "Bonnie Meadow Lane" that was not the same as the past episodes which was "Bonnie Meadow Road" in all the other episodes except for when Rob and Laura were buying the new house beside Jerry and Millie's house.
Other mistake: Evan from the insurance company comes over to ask Laura and Rob several questions but not once does he find out any names from the party. But the next day Buddy, Sally, Mel, Jerry and Millie all get really angry because of Rob and his interrogator just assuming that they stole the watch.
Suggested correction: Evans says he had all the preliminary information from Rob's earlier phone call including the names of the party guests.
The Man from My Uncle - S5-E27
Continuity mistake: When Rob and Harry are in Richie's room, it's bright and sunny outside. Six seconds later, they are in the living room, and it's pitch black outside.
Fifty-Two, Forty-Five or Work - S5-E13
Continuity mistake: Rob tells Sally, Buddy and Mel "It was rough... Out of work, new house, no furniture, a baby on the way, 1 single dime in the bank!" In several other episodes Rob said they either already had a kid, or they were on their way to the hospital in the cab, on their way to the hospital in the back of a laundry truck, or were already at the hospital. They already had furniture in the other episodes when they brought Richie home from the hospital.
Character mistake: Rob is telling Laura about how Buddy and Sally work he says "Sally is the only one who can type with all her fingers." Yet Rob can type with all his fingers and doesn't say anything about that.
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.
The Man from My Uncle - S5-E27
Factual error: The Government Agent says "we want to use your house for base operation for looking at the house across the street. Rob says "Jerry helper!" yet Jerry lives on the same side of the street (closest to the den, across from Rob's bedroom). Someone has their houses mixed up.
Buddy Sorrell, Man and Boy - S5-E22
Other mistake: Rob got a new watch for his birthday a few seasons back. Yet he's still wearing his old watch. And also his watch time says it's 3:00. Rob and Sally would still be at work if it was actually 3:00.
The Great Petrie Fortune - S5-E6
Factual error: Rob tells this lady that the guy that passed away was his great-uncle and that the last time he saw him was when Rob was 12 years old... This is the same Grandpa that was also seen in the episode "What's in a Middle Name" (in this episode in season 5 Richie would be 10 or 11. But the other episode he was supposedly 8).
Suggested correction: You seem to be confused about Hezekiah's relationship to Rob. He is Rob's great-uncle which means he's the brother of Rob's grandfather, the character from "What's in a Middle Name?" (And by the way, the scene in that episode took place before Richie was even born. The fact that they were arguing over his name should have been a clue).
Revealing mistake: Millie (in Rob's dream) tells Jerry (Doc) that "Big Bad Brady is already dead" yet we see that Brady is up there trying to not move, laugh or breathe. He's still alive if his stomach is still going and moving the whole time. Also when he aims his pistol at Rob, he's aiming it at Rob's hat. Not at Rob's arm. Which is where Rob said he got "shot".
Factual error: In the Army or Military it is mandatory that the name tag is worn the same as the Dress Tan/Green/Blue and must be worn in either configuration. Ribbons are worn the same as the Dress Tan/Green/Blue. Special Skill Badges, Distinctive Unit Insignia (Unit Crest) are also worn the same. Rob and everyone else in the army was not wearing a name tag in any of the episodes.
You Ought to Be in Pictures - S5-E28
Deliberate mistake: The movie director tells everyone "ACTION!" Yet Rob stands outside the door and doesn't come in, then he says "uh...action?" Then Rob pokes his head in and asks Leslie "Did you say something?" In "Somebody Has to Play Cleopatra" Rob is the director of the play. He says "Action!" and then Harry (Bob Crane) does not come in on cue several times. Rob also calls Leslie "Liz". (00:15:35 - 00:16:20)
The Bottom of Mel Cooley's Heart - S5-E19
Other mistake: All the extra people in the back aren't talking. There is one pair of people at the table near the wall behind Rob and Mel that keep glancing at them and look very uncomfortable. (00:11:00 - 00:13:00)
Factual error: Rob told Sally and Buddy that he hit "Boom Boom" in the appendix. When we see Rob punch that guy he hit him right in the upper stomach. Rob would have won the boxing match. Because "below the belt" refers to all the area of the body that lies below the line of the opponent's navel, including the groin area, legs, and crotch.
Revealing mistake: While Rob is having a boxing match and Laura is really mad at Rob. I noticed that some of the punches are actually to the hand region when Rob is in the corner and supposedly gets a boxing glove to the face. They aren't hitting each other that hard either.
Continuity mistake: Laura is reading the name of Rob's book "Unimportant Life of Robert F. Petrie" yet in "Fifty-Two, Forty-Five or Work" Rob said his name was "Robert Simpson Petrie"
Fifty-Two, Forty-Five or Work - S5-E13
Other mistake: Right at the beginning of this episode Rob says "9 years ago right in this office... I just came on as head writer 2 months was all... Buddy, Sally and I were sitting at this desk, writing a sketch, and you (Mel) came in with some special news." (so on and so forth with that line.) Rob, Sally and Buddy weren't in "this office" building... Didn't even have the same desk or furniture.