Continuity mistake: When Doug is handing the deodorant back to Arthur the way he holds it changes between shots. (00:06:15)
Continuity mistake: When Tim asks Doug if he wants to tee off back at the start of the hole rather than halfway down the fairway, he is pointing with his golf club. Camera cuts and he isn't. (00:15:35)
Continuity mistake: When the IPS guys are discussing the Superbowl party, one of them takes a drink. He then lowers his can. When the angle changes, the can has changed hands. (00:04:20)
Continuity mistake: When Carrie asks Arthur how a legless dummy will protect her on the subway, her arms are either on the table or off, depending on the shot. (00:10:30)
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)
Continuity mistake: At the start, when Carrie is talking to Arthur about being inseparable she has her jacket over her arm. Camera cuts and now she is putting it on instantly. (00:00:10)
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)
Continuity mistake: When Carrie takes a drink from her cup of tea she is holding her cup with 1 hand in one shot and 2 in a second shot. (00:14:30)
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)
Strike One - S3-E5
Continuity mistake: When Doug has a look at the bumper sticker Spence has, there is one fold in it, but when it cuts there is now three. (00:14:40)
Continuity mistake: When Doug says that there is nothing going on at work, his hands are flat on the table, camera cuts and he's got one up in the air. (00:06:50)
Continuity mistake: When Doug and Carrie are in Deacon's kids' room, Carrie is changing the baby and between shots the baby changes from lying down to sitting up. (00:15:00)
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)
Visible crew/equipment: After Doug gets Arthur out of the house he takes him to a restaurant, and as they both take their seats, the two sets of double tape marks are visible on the carpet under the table. Then, when Doug stands up another small tape mark is visible at his feet. (00:06:30 - 00:08:00)
Frozen Pop - S2-E15
Visible crew/equipment: When Arthur puts his big red jacket on and goes downstairs, Carrie follows and tape markers are visible on the floor by the door. (00:16:30)
Frozen Pop - S2-E15
Continuity mistake: When Doug has just gone back to bed and Arthur walks in, Doug's position on the bed changes instantly. He swaps sides. (00:05:35)
Frozen Pop - S2-E15
Continuity mistake: When Arthur comes in and shuts Doug's window, Doug's hand goes from open to closed between shots. (00:06:00)
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.