Wild Cards - S2-E20
Other mistake: All players' cards were dealt face down in the blackjack game. At one point, the dealer pulled a 20 and immediately collected everyone's chips. The dealer couldn't have known that he beat all players at the table with a 20 when he couldn't see anyone's hand.
Wild Cards - S2-E20
Factual error: In the show, the blackjack players are dealt two cards face down and don't show their hand to the dealer until they either make a hand or bust. In reality, blackjack players in Atlantic City are dealt both cards face up and are never allowed to handle the cards for any reason. If both cards were dealt face down and handled by the players, there would be a strong opportunity for cheating. In addition, if their math wasn't adequate, they might take extra cards that they shouldn't have been dealt.
Wild Cards - S2-E20
Continuity mistake: When Doug calls Carrie to confess, note the phone cable. The loop changes between several shots from a neat loop to an extremely messy loop. (00:20:30)
Wild Cards - S2-E20
Continuity mistake: When Deacon is sat on the bed with all the poker chips, the position of the chips on the bed is constantly changing between shots. (00:14:00)
Wild Cards - S2-E20
Factual error: Deacon is holding an In-N-Out drink cup. In-N-Out is a burger chain only located on the West Coast of the United States. (00:02:00)
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.