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)
Ssiscool
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)
The MinisterTwo 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?"
The MinisterOther mistake: Spence eats some peanut M&M's despite being allergic to peanuts. (00:01:40)
Ssiscool 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)
Ssiscool 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 sits down to read his book, he has his book on his tray. This then disappears as the shot changes. (00:11:20)
Ssiscool 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)
The MinisterRevealing mistake: When Deacon tries the doors on the van, the wall moves, revealing it's not a van but a set. (00:08:30)
Ssiscool Queasy Rider - S2-E1
Continuity mistake: When Doug tells Carrie that he is getting rid of the bike, Carrie has got a fag in her hand and her hand is up by her head. Camera cuts and now her arm is down across her lap. (00:15:40)
Ssiscool 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)
Ssiscool 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)
Ssiscool 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)
Ssiscool 
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)
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.
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.
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)
Ssiscool Character mistake: When Carrie finds Tina, she mentions the "stuff" that Tina listens to at work, and Tina tells her that it's salsa. We know from previous episodes that Carrie likes salsa dancing, so shouldn't she know salsa music?
Queasy Rider - S2-E1
Visible crew/equipment: When Doug comes into the garage and falls over for the first time, a tape marker is visible on the floor. (00:07:05)
Ssiscool Revealing mistake: When they first drive to their class, we see the street lights behind them. When Carrie pulls over to pick up Spence, she turns the steering wheel, but the lights in the back don't turn. (00:07:45)
Ronnie Bischof
Chosen answer: That is most likely the case.
Ssiscool