Deconstructing Carrie - S7-E15
Continuity mistake: While Carrie was being harassed by the construction workers, Doug was watching by looking out the door to the right. In the next shot, you see Carrie through the window, coming in from the left.
Revealing mistake: When Carrie phones Doug at IPS, Doug goes to press the button on the phone for the correct line, but doesn't press any and continues to talk to Carrie. (00:07:40)
Two Thirty - S4-E24
Plot hole: In this episode Arthur scams Deacon and several other parents for phony piano lessons because he doesn't actually know how to play the piano. However, earlier in the series (Art House episode, S1 - E24) we learn that Arthur can play the piano when he temporarily moves out and after his house warming party Doug says to Carrie, "Who knew Arthur could play the piano like that?"
Other mistake: Spence eats some peanut M&M's despite being allergic to peanuts. (00:01:40)

Continuity mistake: When Doug sits down to read his book, he has his book on his tray. This then disappears as the shot changes. (00:11:20)
Soft Touch - S2-E22
Continuity mistake: During the intro to this episode Carrie is trying to park the car. However you can see from the top angle that it's actually Doug driving, not Carrie, during the last attempt when the car finally makes it into the spot. (00:01:05)
Revealing mistake: When Deacon tries the doors on the van, the wall moves, revealing it's not a van but a set. (00:08:30)
Continuity mistake: In this flashback episode, when Doug is shaving his moustache and talking to Deacon by his locker at IPS, Danny Hefferman's name can be seen on a locker. At this time Danny was not working at IPS.
Continuity mistake: When Doug, Carrie, Deacon and Kelly are looking at the damage caused by the accident, the same kid in the black and red hat checking his watch walks by twice. (00:05:10)
Frozen Pop - S2-E15
Visible crew/equipment: At the very beginning, when Carrie walks in, a boom mic is visible above her. It then quickly moves out of shot. (00:00:05)

Continuity mistake: In the scene where Arthur is on the phone with PBS to complain about getting a "Civil War Series" box set, the actual set of tapes changes drastically. When it's on the table and when Carrie brings it over to the counter its a pretty large, has an American flag motif, and says "Civil War" across the top. When it cuts back to it sitting on the counter its a much smaller box with a plain design and says "The Great War" along the bottom. It's obviously a different set, not just the camera angle. (00:14:40)
Revealing mistake: When the guys are watching the game in Doug's bedroom, we see a shot of the TV. If you look closely you can see in the reflection that no-one is on the bed. (00:13:00)
Queasy Rider - S2-E1
Continuity mistake: When Arthur starts telling Doug about when he had a bike, you can see the tv gets switched off. However neither Doug or Arthur turn it off as both of their hands are in screen and the remote is on the table. (00:14:30)
Revealing mistake: In the final scene, Carrie starts to kiss Doug and pushes him onto the bed. The camera angle switches from what would be outside the window to beside the bed. The scene was done in one take from 3 camera angles. As the camera pans left you can see the center window is completely open because they had just pulled the camera out of it and didn't get it closed yet, and you can watch the window be closed by an invisible hand from underneath. (00:28:00)
Continuity mistake: The piano in the living room is ebony in the beginning of the episode. At the end of the episode the piano is brown.
Visible crew/equipment: When Doug calls to the bloke at the bar to get Jill's attention, a boom mic is very visible on screen. (00:13:50)
Other mistake: In outside shots the front door is on the extreme right. Shots from inside the house show the living room on the left and the door in a central position.
Revealing mistake: When Doug and Deacon are driving round trying to find Gabe's Pizzeria, they get into the car and pull out into the road. However if you look at the traffic, they would have hit at least 2 cars in doing so. But they don't, showing it's a projection. (00:14:40)
Continuity mistake: In the pilot episode, we see out of Doug's bedroom window and there is a very sizable gap from their window to the next house. However in later episodes, it's only a couple of feet to the next house.
Queasy Rider - S2-E1
Other mistake: Arthur gives his CV to Doug at the start. You can see it's typed but both Doug and Arthur talk about it being in magic marker. (00:00:30)
Answer: Sara hasn't been mentioned in later episodes, and it suggested in later episodes that she never existed, and that Carrie is an only child. Kevin James stated that the producers couldn't think of an good plots to use with Sara, so they left her out.