Continuity mistake: When Doug is ringing Arthur at the beginning of the episode, there are 2 lunch boxes on top of the lockers behind Doug. During different shots 1 disappears and reappears. (00:00:45)
Continuity mistake: At the start there are 2 letters on the table in front of Arthur. When Doug rings for the 3rd time they have disappeared. (00:00:50)
Continuity mistake: When Arthur walks into the kitchen at the start and picks up the phone, the door is closing. The camera cuts to Doug at IPS, then back to Arthur and the door is still at the same point of closing. (00:00:55)
Audio problem: When Carrie taps Doug's chest and says to go and change, the sound of the taps is out of synch with the motion. Most noticeable with tap 3. (00:02:40)
Continuity mistake: When Kelly says to Deacon "Maybe it's 'cause you're walking late all the time" she has her mug up in the air, camera cuts and it's down on the table. (00:06:25)
Continuity mistake: When the guys are having brunch, Kelly has got her mug in her hand. Camera cuts and her grip has changed on the mug completely. (00:06:40)
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 talking to Deacon outside, Deacon has his arms folded or straight depending on the camera angle. This is before anyone comes out. (00:08:05)
Visible crew/equipment: When Doug is outside talking to Deacon and Arthur opens the kitchen door, as the door swings back you can see all the set lights reflected in the glass. (00:08:20)
Visible crew/equipment: When Carrie come out into the back garden to speak to Doug and Deacon, a boom mic drops into shot very briefly. (00:08:55)
Continuity mistake: This is a very tricky one to spot as it happens as the shot is fading into black to a scene change but it is noticeable without the use of pause and/or slow motion. When Doug and Deacon are outside talking, Carrie comes out and then proceeds to walk back in and and audibly shut the back door. However as Doug and Deacon walk back in as the shot is fading away, the door is wide open. (00:09:30)
Visible crew/equipment: When Doug tells Carrie "eyes off" someone can be seen moving on the stairs behind them due to a foot appearing in shot and shadows moving. However no-one else is at home other than Doug and Carrie. (00:10:40)
Visible crew/equipment: When Deacon shows up with no shoes he steps inside the house and there is a white tape marker visible where he stops. (00:15:20)
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.