Continuity mistake: When Doug spots the chicken he has his gun down by his side in the first shot and raised in the second shot. (00:18:40)
Continuity mistake: When Doug goes to get Carrie's present from the closet her position on the bed changes between shots. (00:05:30)
Hi Def-Jam - S3-E13
Continuity mistake: At the start Carrie is holding an egg in two hands or one hand depending on the camera angle. (00:00:42)
Strike Too - S3-E6
Continuity mistake: At the start when Doug is having his breakfast something appears on top of his pancakes. (00:00:30)
Visible crew/equipment: When Fisker comes down to the drivers area of IPS, there is a white T Mark on the floor. (00:14:20)
Strike Too - S3-E6
Continuity mistake: When Carrie puts her bag on at the start it swaps arms instantly. (00:02:30)
Continuity mistake: When Danny interrupts Deacon and Kelly's dinner the couple retreat to their bedroom, and while Spence mumbles to himself as he clears the plates, in the closeup he places some plates on the pass-through shelf, but those plates have vanished in the next wide shot.
Cheap Saks - S6-E15
Visible crew/equipment: While Doug reaches for the phone when Trish is calling you can see where the kitchen wall is ending on the set. (00:11:53)
Factual error: Doug goes to the doctor for a check up after losing some weight. They live in New York, but the address on the outdoor sign is actually in California. (23101 Sherman Pl).
Visible crew/equipment: Jessica asks Carrie what number they live at - as she does so a tape marker is visible on the floor. (00:06:50)
Maybe Baby - S1-E25
Continuity mistake: When Doug tells Deacon that he and Carrie are trying for a baby, Deacon has both hands on his knees, camera changes and he's got 1 hand and 1 elbow on his knees. (00:09:50)
Continuity mistake: When Danny storms out he is not through the door - the camera changes and the door is closed and Danny is gone. (00:18:20)
Continuity mistake: When Arthur is listing the genres of the film, his legs go from on the floor to one raised and back between shots. (00:02:10)
Hungry Man - S1-E21
Visible crew/equipment: When Arthur accuses Spence of trying to push him out, there is a white taper marker visible on the rug where Arthur stands to accuse him. (00:17:50)
Hungry Man - S1-E21
Visible crew/equipment: When Spence is pacing there are tape markers visible on the floor where he turns. (00:17:20)
Hungry Man - S1-E21
Revealing mistake: When Deacon drops the suit off to Doug, Doug parks the truck up and Deacon gets in, however the outside of the truck is still moving as if Doug is driving. (00:07:50)
Hungry Man - S1-E21
Visible crew/equipment: When Doug explains he's working the double shift a white tape marker is visible on the floor by the front door. (00:03:20)
Hungry Man - S1-E21
Revealing mistake: When Arthur plugs the blender in you can see the wall move. (00:02:25)
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.