Move Doubt - S8-E8
Visible crew/equipment: Season 8, episode 8 "Move Doubt": When Carrie and Doug leave Kelly and Deacon's apartment, you can see the shadow of a boom mic on the wall to their left.
Visible crew/equipment: When Carrie and Doug head out to the garage the first time, a boom mic is reflected in the door's glass. (00:04:05)
Party Favor - S2-E13
Continuity mistake: At the start, Doug has a spatula in one hand and a whisk in the other. Camera does an instant cut and they have swapped hands. This is not to be confused with when he is messing about and you see him swap the items between hands. (00:00:50)
Continuity mistake: When Doug and Carrie are arguing over Arthur having a house, the head on Doug's beer keeps changing size. (00:02:00)
Continuity mistake: When Doug and Carrie are arguing about not having gone out for pizza, Carrie has her pen in her hand, but when it cuts it's now on the desk. (00:10:30)
Visible crew/equipment: When Carrie says about going back in time, a boom shadow can be seen moving over the wall. (00:02:30)
Continuity mistake: When Doug is going into the living room after Carrie has gone in search of Arthur, his left hand is on the door. When he goes through the door, he is opening it with his right hand. (00:14:00)
Visible crew/equipment: When Doug says that Carrie is making progress with her room, a boom shadow can be seen moving along the door. (00:03:30)
Tube Stakes - S2-E5
Continuity mistake: When Doug notices that his TV is missing, he turns and rushes past the coffee table with his cereal in his hands. In the next shot the cereal is on the table.
Queasy Rider - S2-E1
Continuity mistake: When Doug is checking Arthur's CV at the start, the items on the counter keep moving - noticeably the mayo and lid. (00:00:25)
Queasy Rider - S2-E1
Continuity mistake: When Spence is talking to Carrie at the restaurant at the start, Spence has his hands out in front of him. Camera cuts to another angle and now he has his drink in his hand. (00:01:45)
Continuity mistake: When Carrie is taking the shopping out of the bag, the items are constantly moving on the side without being touched. (00:03:30)
Continuity mistake: At the start, Carrie is saying she wants popcorn with the movie and is motioning with 1 hand. Camera cuts and now both arms are outstretched. (00:00:30)
Character mistake: The Doctor tells Carrie what's wrong with Arthur and what they are going to do. When he tells Carrie this, they are in a packed waiting room, completely violating patient confidentiality. (00:08:35)
Revealing mistake: In the kitchen, Deacon asks Doug, "Are we gunna play basketball or what?" while leaning against the counter. In this shot you can see the kitchen wall is on an angle slanting away from the camera. This makes the kitchen look bigger and cuts down on the empty stage space on the wall where the cameras are. (00:07:00)
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.