Continuity mistake: During the first shuffleboard scene, the characters are brightly lit and cast by long dark shadows (indicating early morning or late afternoon), but when you see shots of the shuffle pucks flying into the bleachers, the bleachers' and extras' shadows are cast straight down (indicating noon hour).
Continuity mistake: When Arthur asks Doug for a game of ping pong, a ball suddenly appears under his bat and then disappears and Doug throws him the ball to have the first serve.
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: During both driving scenes, the street lights in the background do not fade away in the distance to indicate they are actually driving forward. When Doug, Carrie and Arthur are pulled over waiting for Spence (and again when waiting for Arthur at Dairy Queen), lights scroll over the car and the sound of a passing vehicle can be heard but no car is seen to pass by or drive away in the distance. (00:07:45)
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: In the episode where Priority Plus is mentioned, after the Priority Plus driver has got Doug Out of the drive through, he gives Doug a lift in his truck. In some shots there is a window on the side of the street. In the window there is no Priority Plus truck visible.
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: From outside shots of Coopers, there are no garbage bins or newspaper boxes in front of the pub. From inside shots, several bins can be seen just outside the glass doors.
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)
Frozen Pop - S2-E15
Continuity mistake: When Carrie is talking to Arthur at the start, Arthur's hands are in his lap in one shot and clasped together in the next. (00:02:45)
Continuity mistake: Deacon states on a few occasions in this episode that him and Doug started at around the same time at IPS. However, in later episodes it's revealed Deacon is senior to Doug by quite a bit in flashbacks to how Doug got his job. (00:10:00)
Continuity mistake: When talking to Doug in the back yard, Carries hands are changing position between instant cuts. In some shots they're together in her lap in others she's holding Doug. (00:04:00)
Court Date - S1-E17
Continuity mistake: When Doug, Carrie and Ritchie are talking about the cop having not called her yet, Doug's hands are either on or off the bottle of beer, and the level of beer/foam changes between shots too. (00:16:30)
Court Date - S1-E17
Continuity mistake: When Arthur storms out saying that was his drug speech, Carrie has her wrists in the table in one shot and under the table in the next. (00:15:10)
Hungry Man - S1-E21
Continuity mistake: At the very end when Carrie walks out the level of foam on Doug's beer bottle changes between shots. (00:21:20)
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.