Other mistake: Carrie describes Susie as "one of her best friends." Earlier in this same season, the episode "Female Problems" was about her not having friends anymore. In fact, in that episode, she spent a whole evening calling any former friend that she could think of. She told Doug that they all had babies, hated her, or she hated them.
Visible crew/equipment: Lighting equipment is visible in the lower left corner of the shot of the outside of the Heffernan home. (00:14:42)
Visible crew/equipment: Doug, Deacon, and Danny are at their lockers towards the end of the episode, and Deacon says, "Me and Danny gotta do another half shift tonight." Camera cuts, and a boom mic can be seen at the top of the screen.
Visible crew/equipment: When Doug and Carrie are talking about the sketch of Carrie on the fridge and Doug says, "Man, he's got some skills" (talking about Major), a boom mic is visible at the top of the screen.
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 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)
Train Wreck - S1-E20
Visible crew/equipment: When Carrie grabs the mail off the floor if you look in the window behind her you can see the pole of a boom mic moving around. (00:12:45)
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)
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)
Visible crew/equipment: When Arthur walks into the living room humming the Happy Birthday tune, as he bends down to pick up the magazine, a camera is visible on the right side of the screen. (00:02:30)
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: While Doug is scraping the windshield in the wide shots, the end of the street backdrop and production equipment are visible at the upper left side of the screen. (00:01:15)
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.