Continuity mistake: When Doug Tells Carrie to pack for Atlantic City the cushion is either on or off her lap. (00:17:15)
Deconstructing Carrie - S7-E15
Continuity mistake: While Carrie was being harassed by the construction workers, Doug was watching by looking out the door to the right. In the next shot, you see Carrie through the window, coming in from the left.
Continuity mistake: The garage door in the outside view has 4 windows. Switch to the inside scene and it has 3.
Food Fight - S4-E13
Continuity mistake: When Spence and Becky arrive near the end, Doug's coat on the floor changes position with no-one touching it. (00:17:20)
Food Fight - S4-E13
Continuity mistake: When Doug is checking the mail while telling Carrie about checking the food twice a week, the letter at the back of the pile is red. Camera changes and now it's a normal envelope. (00:05:30)
Continuity mistake: When Doug is speaking to Spence and Deacon about Carrie throwing up, Spence takes the cap off his beer which reappears a few shots later. (00:02:45)
Continuity mistake: When arguing with Arthur about moving upstairs, Carrie has her hand on a chair or the table depending on the shot. (00:05:50)
Continuity mistake: Arthur throws Doug's pumpkin out near the start and there is no pumpkin on the floor in the kitchen. A few minutes later in the scene, there is pumpkin on the floor in the kitchen. (00:03:40)
No Retreat - S4-E5
Continuity mistake: When Horseback riding Doug is holding on to the straps with either one or two hands depending on the shot. (00:16:50)
Continuity mistake: When Deacon is asking Doug if "Chain of causation" is a legal term, him arm goes from straight to bent between shots. (00:17:20)
Continuity mistake: When Carrie is on the phone to change the insurance cover, her hair is either tucked behind the phone or covering the phone depending on the shot. (00:15:50)
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)
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)
Continuity mistake: When Doug and Deacon both volunteer for the calendar the magazine on the bench is constantly changing position without being touched. (00:05:10)
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)
Continuity mistake: When Carrie realises Doug has been in the pool, the magazine in Doug's hand vanishes instantly. (00:18:20)
Continuity mistake: When talking in the bedroom, Carrie's legs are constantly alternating between on the floor and crossed on the bed. (00:07:20)
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)
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.