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.
Continuity mistake: The lady walks away from Carrie's desk with some flowers. When she does, there are three petals on Carrie's desk which disappear without being touched. (00:06:10)
Soft Touch - S2-E22
Revealing mistake: When Carrie is trying to park, the position of the shadows on the ground is changing drastically between shots. This cannot be attributed to it taking Carrie a long time to park, as the shadows move forward and back. (00:02:00)
Strike Too - S3-E6
Continuity mistake: The writing on the blackboard changes between shots when Doug writes his name. Note the R in Mr. (00:15:10)
Continuity mistake: The baseballs on the stand move apart when Doug picks up the first ball to win Carrie a frog at the boardwalk. (00:17:24)
Soft Touch - S2-E22
Continuity mistake: When Arthur is trying to get Mickey to take a sip of water, Mickey crosses his arms. When the shot changes back to Mickey, he crosses his arms again. (00:15:30)
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)
Other mistake: Carrie describes Susie as "one of her best friends." Earlier in this same season, the episode "Female Problems" was about her not having friends anymore. In fact, in that episode, she spent a whole evening calling any former friend that she could think of. She told Doug that they all had babies, hated her, or she hated them.
Visible crew/equipment: Lighting equipment is visible in the lower left corner of the shot of the outside of the Heffernan home. (00:14:42)
Visible crew/equipment: Doug, Deacon, and Danny are at their lockers towards the end of the episode, and Deacon says, "Me and Danny gotta do another half shift tonight." Camera cuts, and a boom mic can be seen at the top of the screen.
Visible crew/equipment: When Doug and Carrie are talking about the sketch of Carrie on the fridge and Doug says, "Man, he's got some skills" (talking about Major), a boom mic is visible at the top of the screen.
Frozen Pop - S2-E15
Visible crew/equipment: When Arthur puts his big red jacket on and goes downstairs, Carrie follows and tape markers are visible on the floor by the door. (00:16:30)
Frozen Pop - S2-E15
Continuity mistake: When Arthur comes in and shuts Doug's window, Doug's hand goes from open to closed between shots. (00:06:00)
Frozen Pop - S2-E15
Continuity mistake: When Carrie is talking to Arthur at the start, Arthur's hands are in his lap in one shot and clasped together in the next. (00:02:45)
Continuity mistake: Deacon states on a few occasions in this episode that him and Doug started at around the same time at IPS. However, in later episodes it's revealed Deacon is senior to Doug by quite a bit in flashbacks to how Doug got his job. (00:10:00)
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.