Strike One - S3-E5
Visible crew/equipment: After Carrie discovers she can't take a shower because Doug ripped out the shower tiles, when she walks out of the bathroom keep your eye on the window at the right. Just as Doug lifts the hammer a crew member is visible in the bathroom's window (it's not Doug's reflection). (00:17:15)
Strike One - S3-E5
Visible crew/equipment: When Spence's taxi pulls away, a crew member, light screen and stage light can be seen reflected on the window of the taxi. (00:18:10)
Strike One - S3-E5
Continuity mistake: When Doug has a look at the bumper sticker Spence has, there is one fold in it, but when it cuts there is now three. (00:14:40)
Strike One - S3-E5
Revealing mistake: In the kitchen, when Doug tells Carrie he knows the strike will end in 1 or 2 weeks tops because he's a Union Member, the blue shelves/cabinet on the wall behind Doug are positioned properly. Then, when Carrie asks him what the strike issues are, watch as the blue shelves move sideways behind Doug (this wall with blue shelves/cabinet is hinged to provide camera access). (00:13:00)
Strike One - S3-E5
Visible crew/equipment: When it cuts from Doug singing with the barbershop quartet, to Doug and Carrie standing in the garage with the new vehicle, the end of the garage set wall is visible on the left side of the screen. (00:09:35)
Strike One - S3-E5
Visible crew/equipment: When we see the car in the garage for the first time we see the camera start to move. As it does, so a boom shadow can be seen to move over the car. (00:09:20)
Strike One - S3-E5
Other mistake: The salesman calls Doug by his name without Doug telling him his name. His Work ID as shown in other episodes states D. Heffernan. (00:07:20)
Strike One - S3-E5
Visible crew/equipment: When Carrie is trying to return the truck, there are tape markers visible on the floor. They are little white dots. (00:11:35)
Strike One - S3-E5
Continuity mistake: When in the garage, the way Carrie's arms are crossed changes instantly. (00:09:50)
Strike One - S3-E5
Other mistake: When Carrie yells at Doug for ruining the bathroom, she yells when she is at the top of the staircase, and we can still see her legs. There is no way she could see the problems in the bathtub from there. (00:15:20)
Strike One - S3-E5
Continuity mistake: When Carrie says about smelling like the F train she has her hands together in front of her chest. When the camera changes angle, her hands are spread. (00:16:20)
Strike One - S3-E5
Visible crew/equipment: When Doug is listing all the extras for the truck, you can see tape markers on the floor behind them. Specifically, one in between the feet of an extra that is standing behind them. (00:08:50)
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.