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
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)
Hi Def-Jam - S3-E13
Other mistake: When playing poker, Stef says she has all hearts which is a flush. However if you look at the cards she puts on the table, there is a 6 of diamonds and 3 of clubs. Therefore, not a flush. Everyone at the table, (Lou, Mr. Prezants, Deacon, Spencer and Doug) all agree it's a flush. (00:13:30)
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.