Continuity mistake: When Tim and Doug are talking about the pool overlooking the property, the way Tim holds the ball changes between camera cuts. (00:15:00)
Visible crew/equipment: When Doug gets the beach ball, all the stage lights are reflected in it. (00:14:00)
Visible crew/equipment: When Carrie comes back saying she can't swap the flights, there are various tape markers visible on the floor. (00:19:00)
Continuity mistake: When Doug is writing on a board, he holds the board at the end or the top depending on the shot. (00:03:30)
Visible crew/equipment: When Doug arrives at the airport and we see the two gentlemen writing names on a board, everyone has tape markers at their feet. (00:03:20)
Continuity mistake: When Carrie is unpacking the shopping at the start she holds up an empty bag that magically folds itself flat between camera cuts. (00:01:50)
Visible crew/equipment: When Doug says about Kelly being in the wrong he puts his arm up in the air which shows the top of the set and some equipment. (00:14:00)
Continuity mistake: When Carrie turns round and tells Doug that she's telling Kelly about the card, the bottle top on the table is constantly changing position without being touched. (00:11:40)
Visible crew/equipment: When Carrie gives Doug the card, the top of the set is visible behind them. (00:10:40)
Visible crew/equipment: When we first see Doug on a bike in an overhead shot the camera rig is reflected in a car windscreen. (00:17:50)
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)
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)
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)
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 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 Doug spots the chicken he has his gun down by his side in the first shot and raised in the second shot. (00:18:40)
Visible crew/equipment: During Spence and Danny's fight scene, there are a couple of shots where you can see Danny's mic pack on his belt. (00:16:20)
Visible crew/equipment: In the garage, when Spence says "so Deacon" there is a shot of Danny in the chair with a taper marker in front of him. (00:06:30)
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.