Continuity mistake: When Doug first enters the gym, you can see a price tag hanging off of the front of his weight belt. In the shots following this, the price tag is gone. (00:11:10)
Continuity mistake: When we first see Doug at the gym, the sweat stains on his shirt keep changing size. (00:11:30)
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)
Continuity mistake: When Carrie asks Arthur how a legless dummy will protect her on the subway, her arms are either on the table or off, depending on the shot. (00:10:30)
Visible crew/equipment: When Doug says about Carrie's laugh he sits down on the sofa. As he does, part of the set lights are visible above him. (00:15:20)
Continuity mistake: When talking in the bedroom, Carrie's legs are constantly alternating between on the floor and crossed on the bed. (00:07:20)
Visible crew/equipment: When the dummy is on the sofa with Arthur, the stage lights are reflected in its sunglasses. (00:16:00)
Continuity mistake: When Doug and Carrie are in the bedroom discussing the health benefits of Doug losing weight, Carrie's arm is constantly switching from in her lap to on her head. (00:06:50)
Visible crew/equipment: When Arthur is saying about how someone should be able to go out their house and turn left or right, he looks up and the top of the set and the set lights are visible in his glasses. (00:02:45)
Continuity mistake: When talking in the bedroom, the magazines on the bed change from on the bed to on Carrie's ankles. (00:07:20)
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.