Continuity mistake: While at Doug's high school reunion, he and Carrie are dancing. Carrie has her purse on her shoulder. When they go for a beverage, the purse is gone. She was able to put her bun back without having a purse swinging in her face.
Revealing mistake: When Doug runs into the phone when trying to deliver Carrie's package, it's very clear he doesn't touch the phone with his head.
Continuity mistake: In this episode, Doug looks out his bedroom window and sees his parents and Arthur standing on the porch by the front door, but in season one, the episode when Richie sleeps with their neighbor, Carrie and Doug's bedroom window faces the Sacksi bedroom window.
Suggested correction: The window in this episode is the one looking out the front (same wall as headboard), but the one referenced in the episode with Richie is the side window, so a different view.

Revealing mistake: When we see the montage of Doug working as a manager, in one overhead shot you can see the image on the PC is simply stuck on to make it seem like it's on. (00:08:50)

Revealing mistake: Even after receiving the gift basket from the neighbors, the Heffernans are still awakened by their barking dog. When Carrie rushes downstairs Doug stops her at the front door, and the entire left window has been removed (for camera access) from its frame, so there's a large empty hole. (00:13:10)

Visible crew/equipment: While Doug and Carrie are in the kitchen talking about Doug's job, right after Carrie says, "Wait him out 5 or 10 years," in the next shot facing the sink, we can see the end of the kitchen set at the right side of the screen. (00:14:00)

Strike One - S3-E5
Visible crew/equipment: After Carrie discovers she can't take a shower because Doug ripped out the shower tiles, when she walks out of the bathroom keep your eye on the window at the right. Just as Doug lifts the hammer a crew member is visible in the bathroom's window (it's not Doug's reflection). (00:17:15)

Visible crew/equipment: At the start, while Doug and Carrie are in the jewelry store, in the shot of Doug swinging the shopping bags at the overhead surveillance camera, we can see a production camera at the left side of the screen. Then in the next shot, from the POV of the surveillance camera, the edge of the store's set is visible at the right side of the screen. (00:02:05)
Continuity mistake: Carrie says that Deacon does not "drink or smoke." Previous episodes have shown him drinking beer with the guys. Also, in the episode "Friender Bender", it was mentioned that he drank a margarita during dinner at a restaurant.
Factual error: At Shea Stadium, in Queens New York, Carrie asks Arthur if he want a Coolicoo. Carrie then goes to the concession to buy Coolicoo's and tells the guy behind the counter she can see them next to him. However, Coolicoos don't exist at Shea Stadium. They are only available at Dodgers Stadium in L.A.
Continuity mistake: Doug goes to Deacon's to tell him about Kelly wanting to get back together. Deacon is putting on his shoes and in different shots, sometimes his shoe is almost on and then other shots it shows him holding it in his hand about to put it on again.
Visible crew/equipment: Just as Arthur walks in on a mobile phone, a boom mic is visible at the top of the screen. (00:04:00)
Visible crew/equipment: When Arthur comes out the basement singing Silent Night, he stops and waits a few seconds while trying to remember the next line. Carrie prompts him for this and he thanks her and walks off. As he does, the camera changes angle and a tape marker can be seen on the floor where he stopped to remember the next line in the carol. (00:03:30)
Visible crew/equipment: When Doug and Carrie are talking at the start, the green and red baubles give a nice reflection of the stage lights. (00:02:25)

Continuity mistake: When Doug asks Carrie to take a photo of him on the bed, there is nothing on the bed. After she says "stop", 2 items have appeared on the bed that were not in the previous shot. (00:08:45)

Continuity mistake: The leaflet in Carrie's hand at the start vanishes instantly. (00:03:10)

Continuity mistake: When Carrie is on about having never spent that much on a vacation, she has a leaflet in her hand that is open. Camera cuts and now it is partially closed. (00:03:10)

Continuity mistake: After throwing the dummy out the door, Doug kicks his bag out the door too, only for it to reappear a few minutes later. (00:18:20)

Continuity mistake: Doug throws the dummy out the front door and in doing so, knocks a green Jets jacket to the floor. In the next shot the jacket is back on the stand. (00:18:40)