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)
Continuity mistake: In the scene where Arthur is on the phone with PBS to complain about getting a "Civil War Series" box set, the actual set of tapes changes drastically. When it's on the table and when Carrie brings it over to the counter its a pretty large, has an American flag motif, and says "Civil War" across the top. When it cuts back to it sitting on the counter its a much smaller box with a plain design and says "The Great War" along the bottom. It's obviously a different set, not just the camera angle. (00:14:40)
Soft Touch - S2-E22
Continuity mistake: At the beginning, when Carrie is trying to park the car she's wearing a 3/4 sleeve blue top in the closeups, but in the overhead shot of the car for the last attempt when Carrie says that she's cutting it, the driver is not wearing that blue top, the driver is wearing a plaid shirt. (00:01:00)
Continuity mistake: The box of Sgt Salty cereal alternates from open to closed between shots when Doug and Carrie are talking. (00:13:30)
Queasy Rider - S2-E1
Continuity mistake: When Arthur starts telling Doug about when he had a bike, you can see the tv gets switched off. However neither Doug or Arthur turn it off as both of their hands are in screen and the remote is on the table. (00:14:30)
Queasy Rider - S2-E1
Continuity mistake: When Doug tells Carrie that he is getting rid of the bike, Carrie has got a fag in her hand and her hand is up by her head. Camera cuts and now her arm is down across her lap. (00:15:40)
Continuity mistake: In the flashbacks in this episode, Carrie and Doug meet for the first time in a bar, but in the episode "Road Rayge", Carrie mentions a junior high school dance where Doug asked her to dance.
Continuity mistake: When Carrie confronts Arthur about looking in her bag, her bra strap is slightly hidden by her top. Camera cuts to a front view of Carrie then back to behind her. Now her bra strap has moved and is totally visible. Carrie never touched it during this time as we see her hands. (00:12:25)
Continuity mistake: When Doug and Richie are waiting for Spence at the pub, there is a pepper shaker in front of Doug's beer that disappears and reappears. This happens again again after Spence arrives and Rickie is making fun of him. (00:04:15)
Queasy Rider - S2-E1
Continuity mistake: When Arthur is telling Carrie he has got a job, Carrie is putting out paper plates. She puts all three out and then the camera changes angle. When it does, one of the plates has moved across the table and Carrie is seen placing it in position again. (00:10:40)
Continuity mistake: When Doug and Carrie are talking in the kitchen after Doug tried the Sgt. Salty cereal, you can see the cereal box disappear and then reappear on the table behind them. (00:12:45 - 00:13:35)
Continuity mistake: At the start when Carrie walks into the kitchen she opens the door with her right hand. However from the kitchen angle she is opening the door with her left hand and her right is down by her side. (00:03:10)
Continuity mistake: Right at the start, the salad cutlery keeps crossing and uncrossing itself. (00:01:05)
Soft Touch - S2-E22
Continuity mistake: Near the end when Carrie sits on the couch with Doug asking him about the water-filter business, her hand moves instantly from down by her side to on Doug's arm. (00:20:10)
Soft Touch - S2-E22
Continuity mistake: When Doug is desperately trying to sell filters at IPS, he drops four boxes. When he picks them up, the position of one box in his right hand is constantly changing. Blue picture is facing the camera, but when the camera cuts, now Writting is facing where the camera was. Doug has not moved in this time. (00:17:55)
Continuity mistake: At the buffet, the cup that is on the table is either on or off a saucer depending on the shot. (00:06:55)
Continuity mistake: When Doug and Arthur sit down to eat, the cup that is on the table is either by Arthur or by Doug depending on the shot. (00:06:35)
Continuity mistake: When Arthur walks in near the start, Carrie is looking at him. Camera cuts and she is now looking in the totally opposite direction.
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.