Continuity mistake: Carrie cuts Kirby's burger in half with a knife in her right hand. Camera cuts and a fork has appeared in her left hand. (00:10:30)
Continuity mistake: When Carrie is serving up the burgers for dinner, she places one on Kirby's plate. Camera cuts to Kirby sitting down and the burger has vanished. (00:10:25)
Strike One - S3-E5
Continuity mistake: When in the garage, the way Carrie's arms are crossed changes instantly. (00:09:50)
Continuity mistake: When Doug and Carrie are in the bedroom discussing the health benefits of Doug losing weight, Carrie's arm is constantly switching from in her lap to on her head. (00:06:50)
Continuity mistake: The first time Doug throws a ball at the bottles, we see one bottle remain lay down on the stand. Camera cuts and this bottle has disappeared. (00:18:00)
Continuity mistake: The guy on the stall puts 3 balls down in front of Doug in a line. Doug picks up the ball furthest from the guy. Camera cuts and now Doug has the ball closest to the guy. (00:17:30)
Frozen Pop - S2-E15
Continuity mistake: When Doug goes back into the house at the start he opens the door with his right hand. Camera cuts to inside the house and now it's his left hand on the door handle. (00:01:35)
Continuity mistake: When they are talking about Carrie only having one good ovary, the napkin under Doug's hand keeps changing position. (00:15:10)
Continuity mistake: Doug gets into a mess with the sellotape wrapping Carrie's Christmas present. However when she walks downstairs it's on the table, absolutely fine. (00:02:20)
Continuity mistake: The bag Doug puts on Arthur's hospital table is a lot bigger than the bag he got at Gabe's. We know it's not a different bag as he ran from Gabe's, and the bag says Gabe's on it. (00:19:00)
Continuity mistake: When scooping the ice creams for Arthur, Doug scoops pineapple, then banana, from the open case. He then finds lemon, but has to open the case again. (00:17:45)
Mean Streak - S4-E3
Continuity mistake: When sat at the table at the start, the bottle top keeps changing position in relation to the edge of the table. (00:03:00)
Continuity mistake: In the scene where Carrie and Doug are in the kitchen and Carrie is explaining why she wants to quit school, she fills a glass of water to the top of the glass. A few shots later, she sets the glass down on the counter without taking a drink and it is less than half full.
Continuity mistake: When Doug is ringing Arthur at the beginning of the episode, there are 2 lunch boxes on top of the lockers behind Doug. During different shots 1 disappears and reappears. (00:00:45)
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.