Continuity mistake: When Doug is putting lipstick on Carrie, the way she is holding her arms changes between shots (crossed then uncrossed). (00:14:50 - 00:15:40)
Continuity mistake: When Carrie takes Doug into the back yard to yell at him, after she is done swinging at him, she puts her hand up to her chin. First it's her left, then right. It changes between shots. Each time the camera goes back to her it happens.
Mean Streak - S4-E3
Continuity mistake: When sat at the table at the start, the bottle top keeps changing position in relation to the edge of the table. (00:03:00)
Mean Streak - S4-E3
Continuity mistake: When Doug is talking O'Boyle about the old guys, the time on the clock goes back. (00:05:30)
Continuity mistake: When Doug says he was reaching for a fig newton, the way Carrie is stood changes between shots. Note her right arm. (00:04:50)
Continuity mistake: When Doug, Carrie, Deacon and Kelly are looking at the damage caused by the accident, the same kid in the black and red hat checking his watch walks by twice. (00:05:10)
Continuity mistake: At the accident scene when Deacon asks to have a picture taken with him and Doug, the same couple walks by three times. (00:05:30)
Continuity mistake: When Spence and Kirby are talking about why Spence can't make him a PB&J sandwich, the way Kirby holds the red action figure keeps changing. (00:06:15 - 00:06:55)
Continuity mistake: When Doug, Carrie, Deacon and Kelly are at Coopers, the man in the blue shirt who is talking to the women sitting at the table behind them appears, disappears, walks off and then reappears again during this scene. (00:08:20 - 00:10:40)
Continuity mistake: When Doug, Carrie, Deacon and Kelly are at Coopers talking about the auto-repair bill, Carrie's menu instantly switches from on the table to in her lap and then continues to switch depending on the shot. (00:08:30 - 00:09:10)
Continuity mistake: When looking at the quote for the repair bill, its position on the table in relation to Kelly's menu is constantly changing. (00:08:40)
Continuity mistake: The way Carrie is standing and holding the banana and pop-tart changes as Doug admits that he was trying to look into the strip club, not reaching for a Fig Newton. (00:15:15)
Continuity mistake: When Deacon is asking Doug if "Chain of causation" is a legal term, him arm goes from straight to bent between shots. (00:17:20)
Continuity mistake: After Spence and Kirby's arm wrestle, the way Spence holds the action figure keeps changing between shots. (00:51:10 - 00:51:55)
Continuity mistake: When Kirby says that Spence is scared of peanuts and calls him "The Scaredinator", his hands are empty and his arms are folded - then in the next shot he is instantly holding the red action figure again. (00:51:40)
No Retreat - S4-E5
Continuity mistake: During the opening scene in the backyard, Deacon finishes his beer and puts it down. In the next shot of Deacon he is holding the beer again. (00:00:10)
No Retreat - S4-E5
Continuity mistake: When Doug tells Carrie at the start he is telling his jet ski story, the tongs he's holding swap hands instantly. (00:00:45)
No Retreat - S4-E5
Continuity mistake: When Horseback riding Doug is holding on to the straps with either one or two hands depending on the shot. (00:16:50)
No Retreat - S4-E5
Continuity mistake: When horseback riding, the track behind them is constantly changing. For example, when Doug hits the tree, the tree then vanishes. (00:17:40)
Continuity mistake: At the store, Doug picks up 5 or 6 bags of sweets. Most noticeable is 2 yellow bags. Camera cuts and they have disappeared. (00:01:05)
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.