Cheap Saks - S6-E15
Continuity mistake: At the art gallery, the way Doug is holding the program instantly changes a couple times; arms crossed/uncrossed, program folded/unfolded. (00:02:20)
Window Pain - S5-E2
Revealing mistake: When Arthur jumps over the turnstile at the subway where Spence works you can see it is a stuntman wearing the same outfit as Arthur. (00:37:15)
Continuity mistake: At the beginning during dinner, Carrie hands Doug the salad bowl, then puts the spoon into the bowl and hands it to him again in the next shot. (00:02:25)

Continuity mistake: When Doug goes to meet up with Ray, Richie zips up his jacket. In the next shot his jacket is unzipped. (00:06:20)
Continuity mistake: In episodes that show the outside of the IPS building, there are some shots that show a pay phone outside of the building, then other shots where the pay phone is missing.
Continuity mistake: The door to the house is on a corner. However, in the interior shots, they have a window each side of the door.
Other mistake: When Doug is drawing a picture to explain to the nurse why he is there, a man purchases a beverage from the "Hot Drinks" machine behind Doug. The drink is ready unrealistically fast and the man immediately takes a sip from an obviously empty cup. Those machines produce notoriously hot beverages, so if the machine actually worked the man would have scalded himself.
Continuity mistake: When Carrie says that Doug is losing brain cells in the garage due to fumes, the way she holds the tickets changes instantly. (00:12:20)
Revealing mistake: Carrie comes into the kitchen, visibly hot and sweaty, and says, "Could it be any hotter?" Doug also has a sweat stain on his back and they stick their heads in the freezer. Suddenly Arthur walks in and says, "Do I have the word pushover on my forehead?" Arthur is wearing a thick shirt tucked into long pants and yet is not sweaty. At his age he would be more visibly drained from the heat than both Carrie and Doug. This happens again later in the episode in the garage.
Other mistake: Doug says in 4-11 "Repo Man" that he doesn't know when Carrie is in bed or not. However in this episode he states that he can't sleep unless someone is next to him. (00:01:10)
Big Dougie - S2-E21
Revealing mistake: When Doug is jogging in the marathon he is casting three shadows in different directions. Also, the female jogger behind him appears to be in good shape but is still jogging as dramatically slow as Doug. (00:19:20)

Continuity mistake: Carrie and Arthur are talking about Carrie making a Thanksgiving meal, and as they are talking the frozen meals in Carrie's trolley change position between shots. (00:03:10)
Deliberate mistake: At the beginning of the episode, when Doug and Carrie are in the shower, you see their silhouettes. The first mistake is that for the silhouettes to show like that they have to be evenly backlit which wouldn't make sense in the shower. The second mistake is a little more subtle; you can see the outline where the actor's bathing suits are (inevitably) slightly larger than the bodies. There is also a slight darkening in the areas where the bathing suits cover skin. (both of these things are much easier to see on Carrie than Doug because of her smoother figure and skin tone).
Emotional Rollercoaster - S8-E19
Visible crew/equipment: When Carrie steals Doug's grabber then leaves the kitchen, a boom mic shadow moves on the cupboard beside Doug twice. (00:05:25)
Thanks Man - S6-E9
Other mistake: When Deacon's youngest son says "is that man going to freeze, daddy" you can see the older son mouthing the lines. (00:06:16)