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)
Soft Touch - S2-E22
Revealing mistake: When Carrie is trying to park, the position of the shadows on the ground is changing drastically between shots. This cannot be attributed to it taking Carrie a long time to park, as the shadows move forward and back. (00:02:00)
Strike Too - S3-E6
Continuity mistake: The writing on the blackboard changes between shots when Doug writes his name. Note the R in Mr. (00:15:10)
Continuity mistake: The baseballs on the stand move apart when Doug picks up the first ball to win Carrie a frog at the boardwalk. (00:17:24)
Soft Touch - S2-E22
Continuity mistake: When Arthur is trying to get Mickey to take a sip of water, Mickey crosses his arms. When the shot changes back to Mickey, he crosses his arms again. (00:15:30)
Wild Cards - S2-E20
Continuity mistake: When Doug calls Carrie to confess, note the phone cable. The loop changes between several shots from a neat loop to an extremely messy loop. (00:20:30)
Wild Cards - S2-E20
Continuity mistake: When Deacon is sat on the bed with all the poker chips, the position of the chips on the bed is constantly changing between shots. (00:14:00)
Strike One - S3-E5
Visible crew/equipment: When the salesman walks off from Carrie, the top of the set is visible on the left side of the screen. (00:10:30)
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.