Revealing mistake: When Doug and the rest are at a ballgame, the man sitting behind them is eating a hot dog. Actually he's pretending to eat, it never shows any bite marks and the guy is pretending to chew it.
Continuity mistake: At the ball game right before Carrie gets to the front of the concession line, there is a woman right behind here followed by a man. When she gets to the front of the line, the extras behind her have switched.
Continuity mistake: When Ritchi and Spence are at the cafe, Spence pours the remainder of the pitcher into his cup. The shot goes back to him, and it appears he took a large sip because his cup is near empty. When Doug and Deacon come in, Spence's glass is almost full again.
Visible crew/equipment: Stage lights can be seen reflecting off the fake apples in the table center-piece at the hotel. (00:02:25)
Dire Strayts - S2-E8
Visible crew/equipment: When Doug says about watching the game at his on the big screen, a boom mic drops into shot very quickly. (00:01:45)
Dire Strayts - S2-E8
Continuity mistake: When Doug talks about grown men not being able to watch the game, the amount of head on his beer changes instantly. (00:02:40)
Dire Strayts - S2-E8
Continuity mistake: When Doug is talking to Ray at the table, the position of his beer changes between shots. Watch the label. (00:02:45)
Dire Strayts - S2-E8
Visible crew/equipment: When Carrie asks what Deborah is like, on the cupboard door above Doug you can see the reflection of a boom mic moving around. (00:04:45)
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.