Revealing mistake: When Deacon tries the doors on the van, the wall moves, revealing it's not a van but a set. (00:08:30)
Revealing mistake: In the final scene of the episode, Arthur is searching for used bottles of nasal spray. He empties the contents of the trash can on the kitchen floor and finds one after sifting through the trash. However, the bottle had already been positioned on the floor next to the trash can before he picked up the trash can so it would be easy to find when the trash was emptied on the floor.
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)
Revealing mistake: When Carrie knocks the cards over at the start, some stay in the pyramid shape despite being knocked over, revealing the cards are glued together. (00:03:15)
Revealing mistake: Both times when you see an overview of the bridge, it's the same clip being used. (00:07:10)
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.