Soft Touch - S2-E22
Continuity mistake: Near the end when Carrie sits on the couch with Doug asking him about the water-filter business, her hand moves instantly from down by her side to on Doug's arm. (00:20:10)
Continuity mistake: When Doug and Deacon are talking about Doug wearing a disguise to the concession stand, There are two people on the loading bay holding a parcel. Camera cuts and this parcel is no longer in their hands. (00:13:00)
Continuity mistake: In the scene where Arthur is on the phone with PBS to complain about getting a "Civil War Series" box set, the actual set of tapes changes drastically. When it's on the table and when Carrie brings it over to the counter its a pretty large, has an American flag motif, and says "Civil War" across the top. When it cuts back to it sitting on the counter its a much smaller box with a plain design and says "The Great War" along the bottom. It's obviously a different set, not just the camera angle. (00:14:40)
Continuity mistake: When Arthur tells Carrie that he has jury duty, Carrie places her used coffee mug on the counter beside the mug tree, then her used mug vanishes, the mugs hanging on the tree change, and the coffeemaker moves. (00:04:30)
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)
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)
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)
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)
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.