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)
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 Holly walks in at the start, a tape marker is visible on the floor. (00:09:10)
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.