Soft Touch - S2-E22
Visible crew/equipment: When Doug and Carrie go to get up from having dinner with Saskies, tape markers are visible on the floor by their chairs. (00:05:30)

Frozen Pop - S2-E15
Continuity mistake: When Doug goes back into the house at the start he opens the door with his right hand. Camera cuts to inside the house and now it's his left hand on the door handle. (00:01:35)
Queasy Rider - S2-E1
Revealing mistake: We see Doug crash into the fridge 3 times, thus implying that it's 3 times he's crashed. However it is the same clip used for all 3 crashes. (00:13:40)

Queasy Rider - S2-E1
Visible crew/equipment: When Doug and Carrie are arguing over the bike a white tape marker can be seen on the floor. (00:09:20)
Strike One - S3-E5
Other mistake: When Carrie yells at Doug for ruining the bathroom, she yells when she is at the top of the staircase, and we can still see her legs. There is no way she could see the problems in the bathtub from there. (00:15:20)
Visible crew/equipment: In the opening scene, when Doug almost sits on Arthur, you can see part of the blue mat that Doug rolls Arthur off the couch on to.
Continuity mistake: When they are talking about Carrie only having one good ovary, the napkin under Doug's hand keeps changing position. (00:15:10)

Continuity mistake: Doug gets into a mess with the sellotape wrapping Carrie's Christmas present. However when she walks downstairs it's on the table, absolutely fine. (00:02:20)
Continuity mistake: The bag Doug puts on Arthur's hospital table is a lot bigger than the bag he got at Gabe's. We know it's not a different bag as he ran from Gabe's, and the bag says Gabe's on it. (00:19:00)
Continuity mistake: When scooping the ice creams for Arthur, Doug scoops pineapple, then banana, from the open case. He then finds lemon, but has to open the case again. (00:17:45)
Mean Streak - S4-E3
Continuity mistake: When sat at the table at the start, the bottle top keeps changing position in relation to the edge of the table. (00:03:00)
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.