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)
Soft Touch - S2-E22
Revealing mistake: When Carrie is trying to park, the position of the shadows on the ground is changing drastically between shots. This cannot be attributed to it taking Carrie a long time to park, as the shadows move forward and back. (00:02:00)
Wild Cards - S2-E20
Continuity mistake: When Doug calls Carrie to confess, note the phone cable. The loop changes between several shots from a neat loop to an extremely messy loop. (00:20:30)
Wild Cards - S2-E20
Continuity mistake: When Deacon is sat on the bed with all the poker chips, the position of the chips on the bed is constantly changing between shots. (00:14:00)
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)
Soft Touch - S2-E22
Continuity mistake: When Arthur is trying to get Mickey to take a sip of water, Mickey crosses his arms. When the shot changes back to Mickey, he crosses his arms again. (00:15:30)
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)
Soft Touch - S2-E22
Continuity mistake: At the beginning, when Carrie is trying to park the car she's wearing a 3/4 sleeve blue top in the closeups, but in the overhead shot of the car for the last attempt when Carrie says that she's cutting it, the driver is not wearing that blue top, the driver is wearing a plaid shirt. (00:01:00)
Queasy Rider - S2-E1
Visible crew/equipment: When Doug comes into the garage and falls over for the first time, a tape marker is visible on the floor. (00:07:05)
Queasy Rider - S2-E1
Revealing mistake: When Doug comes in at the start and says he has been riding Ritchie's hog, all the stage lights can be seen in Carrie's wine glass. (00:02:20)
Continuity mistake: At the buffet, the cup that is on the table is either on or off a saucer depending on the shot. (00:06:55)
Continuity mistake: When Doug and Arthur sit down to eat, the cup that is on the table is either by Arthur or by Doug depending on the shot. (00:06:35)
Queasy Rider - S2-E1
Continuity mistake: When Arthur gets the iron, he has it down by his side. Camera cuts and now it's up in front of his chest. (00:06:30)
Queasy Rider - S2-E1
Continuity mistake: When Carrie says to Doug that he can't have a bike, her hand are behind her back. Camera cuts and now her bag is on her shoulder and her hands are on her bag. (00:03:00)
Dire Strayts - S2-E8
Continuity mistake: When Doug is talking to Ray at the table, the position of his beer changes between shots. Watch the label. (00:02:45)
Dire Strayts - S2-E8
Continuity mistake: When Doug talks about grown men not being able to watch the game, the amount of head on his beer changes instantly. (00:02:40)
Queasy Rider - S2-E1
Continuity mistake: When Doug starts to explain to Carrie about getting the bike, he has his hands on the edge of the back of the chair. Camera cuts and now they have moved close together in the middle of the chair. (00:07:55)
Queasy Rider - S2-E1
Continuity mistake: As Doug is telling Carrie he hates the bike, his beer and crisps vanish instantly from the sofa. (00:19:20)
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: 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.