Tank Heaven - S6-E21
Continuity mistake: In the scene where Danny has just taken the "nucleus" nacho chip, after Carrie walks in, the chip in Danny's hand keeps changing between shots, then disappears altogether almost instantly and his arms are folded when he begins his next line. (00:02:30 - 00:03:25)
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)
Continuity mistake: In front shots of the house you see that the garage is in the front and opens to the street, but the garage door is behind the house entirely. It seems to open in a back alley or private entrance way. The way it is shown in establishing shots, it can not be open to the front street at the front of the house.
Fixer Upper - S1-E12
Continuity mistake: In "Richie's Song" Doug asks Spence if the M&Ms Spence found under the seat in the car are regular or peanut, Spence answers peanut, and Spence then eats them. In this episode, Spence somehow isn't allergic to peanuts. (00:08:10)
Continuity mistake: In many episodes, scenes are shot on the front porch. It is often shown as a large porch that spans a great deal of the front of the house. But shots of the house exterior from a distance show a small set of stairs with very little space near the door. This isn't a porch on the back of the house as it has been shown to only be door to a small yard.

Continuity mistake: When Doug first enters the gym, you can see a price tag hanging off of the front of his weight belt. In the shots following this, the price tag is gone. (00:11:10)
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)
Continuity mistake: In the scene where Doug's father is shutting off the alarm, he does not enter 2965. We know this is the proper code, because it is Doug's birthday, and it worked when he entered it. It looks like he maybe enters 1459.
Continuity mistake: In this episode, when Doug and Carrie are taking an adult literature class together, Doug comes down the stairs with his book in his hand, but when he sits on the couch he only has his book pillow and reading lamp, and runs back upstairs to get his book.
Continuity mistake: When Carrie takes Doug into the back yard to yell at him, after she is done swinging at him, she puts her hand up to her chin. First it's her left, then right. It changes between shots. Each time the camera goes back to her it happens.
Continuity mistake: Just as Doug persuades Deacon to go with him to Carrie's birthday dinner, his position changes completely. (00:10:20)
Continuity mistake: In the flashbacks in this episode, Carrie and Doug meet for the first time in a bar, but in the episode "Road Rayge", Carrie mentions a junior high school dance where Doug asked her to dance.
Continuity mistake: When Sara is in the shower you can see in her shadow, creases from her swimsuit. (00:16:30)

Continuity mistake: At the store, Doug picks up 5 or 6 bags of sweets. Most noticeable is 2 yellow bags. Camera cuts and they have disappeared. (00:01:05)
Continuity mistake: When Carrie confronts Arthur about looking in her bag, her bra strap is slightly hidden by her top. Camera cuts to a front view of Carrie then back to behind her. Now her bra strap has moved and is totally visible. Carrie never touched it during this time as we see her hands. (00:12:25)
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.
Fixer Upper - S1-E12
Continuity mistake: When Spence realises he's eating peanuts, he steps behind the bench he was sitting on, but in the next shot he is in the front of the bench. (00:08:30)

No Orleans - S4-E16
Continuity mistake: Doug made a blue snowcone in the kitchen and then goes into the living room to talk to Arthur. When he crosses the door in to the living room, the initially full snow cone is now almost gone. (00:02:05)
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.