Dire Strayts - S2-E8
Visible crew/equipment: When Carrie storms out into the back yard, Doug follows. When he does, the kitchen door stays open and if you look at the glass it reflects all the stage equipment above the set in the kitchen. (00:07:00)
Frozen Pop - S2-E15
Continuity mistake: When Doug has just gone back to bed and Arthur walks in, Doug's position on the bed changes instantly. He swaps sides. (00:05:35)
Frozen Pop - S2-E15
Continuity mistake: When Carrie is telling Arthur to move upstairs, the blanket Arthur has got changes position instantly. (00:02:40)
Revealing mistake: When driving to find the dog, neither Doug nor Carrie's hair is blowing in the wind - even when they're on the back of the convertible. (00:18:00)
Frozen Pop - S2-E15
Visible crew/equipment: When Doug goes to scrape the car, a stage light is reflected in the iced up windows. (00:01:05)
Soft Touch - S2-E22
Continuity mistake: At the end when Carrie is telling Doug not to take any more shots, she has one hand on Doug's arm. Camera cuts and she now has two hands on his arm. (00:19:25)
Soft Touch - S2-E22
Continuity mistake: At the start, when Carrie is trying to park, the same clip is shown. The same people walk by. (00:00:30)
Soft Touch - S2-E22
Continuity mistake: When Doug is asking Carrie about the water, she puts a glass down and the level of water in both glasses is significantly different. Camera cuts and they are level. (00:11:10)
Soft Touch - S2-E22
Continuity mistake: When Carrie is asking Doug why he likes it at the neighbors, her arms are on her hips. Camera cuts and now they are straight down at her side. (00:08:40)
Soft Touch - S2-E22
Continuity mistake: When Doug and Carrie are arguing about selling filters, the bed covers keep changing place. Note the position in regard to the jeans. (00:09:05)
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.