
Continuity mistake: When Doug is ringing Arthur at the beginning of the episode, there are 2 lunch boxes on top of the lockers behind Doug. During different shots 1 disappears and reappears. (00:00:45)

Continuity mistake: At the start there are 2 letters on the table in front of Arthur. When Doug rings for the 3rd time they have disappeared. (00:00:50)
Continuity mistake: Right at the start when Carrie gives a sigh, she shuts the menu. In the next shot it's back open. (00:00:25)
Continuity mistake: At the dinner table while talking about being obscure at work, Doug starts pouring his beer into a glass. But immediately in the next shot he is finished pouring and both bottle and glass are on the table. A moment later he picks up the beer and pours it into the glass a second time. (00:03:45)
Visible crew/equipment: When Doug is talking on the phone, the shadow of a boom mic moves on the wall behind him. (00:00:20)

Continuity mistake: At the beginning Carrie is dishing out potatoes from a bowl with a large black spoon, and as the camera changes angles her arm has not moved and she is now holding a small fork getting chicken from a different bowl. (00:01:40)
Continuity mistake: When Carrie is reading from the leaflet, the way she holds it changes depending on the shot. (00:17:35)
Visible crew/equipment: When Doug is lying on the floor with the phone on him, the camera zooms in and you can see a boom arm reflected in the phone. (00:19:35)
Continuity mistake: When Doug says to Carrie that he doesn't even know her anymore, Carrie's laptop and books are open over the desk. However when the camera cuts to her standing up, she has got the laptop folded up and her books in her arms instantly. (00:10:35)

Continuity mistake: At the start of the episode when Arthur is on about kissing ass, the way his napkin is positioned constantly changes. (00:03:45)

Continuity mistake: Doug sits down near the start after getting a drink and proceeds to pour a drink. When it cuts he has instantly stopped pouring the drink. (00:03:40)

Continuity mistake: At the start when Arthur is on about Al Gore, he has chicken in his hands, but when the camera cuts, he now has a fork and napkin. (00:01:35)

Visible crew/equipment: When Doug is outside talking to Deacon and Arthur opens the kitchen door, as the door swings back you can see all the set lights reflected in the glass. (00:08:20)

Continuity mistake: When Kelly says to Deacon "Maybe it's 'cause you're walking late all the time" she has her mug up in the air, camera cuts and it's down on the table. (00:06:25)
Continuity mistake: When Arthur walks into the kitchen at the start and picks up the phone, the door is closing. The camera cuts to Doug at IPS, then back to Arthur and the door is still at the same point of closing. (00:00:55)
Visible crew/equipment: When Doug sneaks out of Carrie's house and finds her having a cigarette by the car, a boom mic shadow can be seen on the bush beside Doug. (02:53:45)
Continuity mistake: When Carrie is sitting at the table talking to Doug about not finishing school, her hand is beside the text book and then instantly holding it from underneath in the next shot. (00:10:35)
Continuity mistake: When Carrie is having lunch with the lawyers from her office, she is holding a cup and then instantly holding a napkin in the next shot. The cup and napkin switch again depending on the shot. (00:03:10)
Continuity mistake: When Doug and Carrie are arguing about not having gone out for pizza, Carrie has her pen in her hand, but when it cuts it's now on the desk. (00:10:30)
Continuity mistake: When Doug and Carrie are in Deacon's kids' room, Carrie is changing the baby and between shots the baby changes from lying down to sitting up. (00:15:00)
Answer: To answer the question directly. Carrie and Doug do not have a biological child during the show's main run. In season 3 or 4 finale (cant remember which) Carrie has a miscarriage. Later on in the show they find out Carrie has 1 working ovary. Thus reducing the chance of them conceiving. By the final season, they couple agree to adopt from China and go to collect their child in the show's final episode. While on the flight back from China it's revealed that Carrie is once again pregnant. However the last scene of the show is a flash forward showing that Carrie goes full term with that child and they are struggling with both kids.
Ssiscool