Visible crew/equipment: When Doug says he doesn't want to look after Arthur in the bedroom, there are 4 tape markers visible on the floor at the foot of the bed. (00:14:30)
Continuity mistake: When arguing with Arthur about moving upstairs, Carrie has her hand on a chair or the table depending on the shot. (00:05:50)
Continuity mistake: When Carrie is on the phone to change the insurance cover, her hair is either tucked behind the phone or covering the phone depending on the shot. (00:15:50)
Visible crew/equipment: Carrie begs Arthur to move upstairs, when she does, a tape marker is visible on the floor by the stairs to the basement. (00:05:30)
Visible crew/equipment: When Carrie walks into the bedroom at the start, 2 tape markers are visible on the green carpet. (00:06:55)
Continuity mistake: When arguing about who is going to die first, the amount of whipped cream around Doug's mouth changes instantly. (00:19:20)
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 ★
Adding on to this answer, I read somewhere that producers were afraid of the show having a "before baby" feeling and then an "after baby" feeling. Some fans feel that main characters, or the show in general, decline in quality after a major change. For example, Jesse and Rebecca on "Full House" after they had twin sons, and Daphne on "Frasier" after she married Niles.