Fixer Upper - S1-E12
Continuity mistake: When Doug is talking to Spencer in the subway, the people in the line behind him change instantly from 2 men to 1 man and 1 woman. (00:19:30)
Head First - S1-E6
Continuity mistake: When the gang walk into Coopers, a woman and man are talking outside on the street. When the camera changes to focus on Arthur a second man has appeared next to the other two and should have been visible in the first shot. (00:03:40)
Continuity mistake: When making a PB&J sandwich, the jar of peanut butter rotates by itself. Note the label. (00:09:30)
Continuity mistake: When Doug falls off his chair his right arm is on the floor in one shot and on the desk part of the chair in the next. (00:09:10)
Maybe Baby - S1-E25
Continuity mistake: When Doug sits down with Arthur in the night, the magazine on the table changes between shots. (00:11:50)
Hungry Man - S1-E21
Continuity mistake: At the start Arthur goes from cutting bananas to having his hands on the side in between instant cuts. (00:01:10)
Train Wreck - S1-E20
Continuity mistake: When Arthur is rewriting his epitaph, the pad and pencil keep moving between shots. (00:12:10)
Train Wreck - S1-E20
Continuity mistake: When Julie goes to get her jacket, Doug's board swaps hands instantly. (00:03:40)
Continuity mistake: At the end, the shawl around Carrie's shoulder is either covering her shoulder or not depending on the shot. (00:20:50)
Continuity mistake: When Arthur sits down to talk about the deodorant with Doug, Doug's hand is flat on the table. Camera changes and it's now on the doughnut box. (00:11:00)
Continuity mistake: At the start, Carrie is saying she wants popcorn with the movie and is motioning with 1 hand. Camera cuts and now both arms are outstretched. (00:00:30)
Revealing mistake: When Doug stops to tie his shoe outside the car dealership and Carrie walks up to grab him, you can see the fake back-drop sway with her motion. (00:08:35)
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.