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)
Visible crew/equipment: The second time Doug pulls up at the toll booth, stage lights and equipment are reflected in the car's paintwork. (00:07:20)
Visible crew/equipment: During the drag race at the end, several times on the van you can see camera shadows. (00:19:10)
Continuity mistake: In the scene where Spence is entering the place his girlfriend works, he is pushing the door in. When the camera angle switches he is pulling the door open.
Continuity mistake: When Carrie is reading from the leaflet, the way she holds it changes depending on the shot. (00:17:35)
Visible crew/equipment: When Doug is lying on the floor with the phone on him, the camera zooms in and you can see a boom arm reflected in the phone. (00:19:35)
Continuity mistake: When Doug says to Carrie that he doesn't even know her anymore, Carrie's laptop and books are open over the desk. However when the camera cuts to her standing up, she has got the laptop folded up and her books in her arms instantly. (00:10:35)
Continuity mistake: At the start of the episode when Arthur is on about kissing ass, the way his napkin is positioned constantly changes. (00:03:45)
Continuity mistake: Doug sits down near the start after getting a drink and proceeds to pour a drink. When it cuts he has instantly stopped pouring the drink. (00:03:40)
Continuity mistake: At the start when Arthur is on about Al Gore, he has chicken in his hands, but when the camera cuts, he now has a fork and napkin. (00:01:35)
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)
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.