Party Favor - S2-E13
Continuity mistake: When Doug is mimicking the Japanese chef, the towel on the side moves positions without being touched. (00:01:00)
Continuity mistake: Near the end when the Heffernans, Palmers, and "Shmenkmans" are having dinner and are in conversation, Carrie is shown sitting extremely close to Abby, who is on Carrie's left. But in shots in the middle of the conversation, there is significant empty space to Carrie's left.
Dire Strayts - S2-E8
Continuity mistake: When the women come into the bedroom, Ray's hand goes from flat to raised on the bed. (00:13:20)
Continuity mistake: When Doug and Arthur are sat at the dinner table, Arthur's hands go from on the table to clasped between shots. (00:07:45)
Party Favor - S2-E13
Continuity mistake: At the beginning when Doug is putting his jacket on to go outside to scrape frost off the car, the lamp in the corner of the living room is off. In the next shot from outside the lamp is instantly on and when can see Carrie did not turn it on. (00:00:50)
Continuity mistake: At the ball game right before Carrie gets to the front of the concession line, there is a woman right behind here followed by a man. When she gets to the front of the line, the extras behind her have switched.
Continuity mistake: When Doug and Ritchie are waiting for Spence, the amount of beer in Doug's glass keeps changing. (00:04:30)
Dire Strayts - S2-E8
Continuity mistake: When Carrie is in the attic and notices the rat, the cobweb that is by her head disappears instantly. (00:17:05)
Dire Strayts - S2-E8
Continuity mistake: When Doug and Carrie are arguing just before Ray and Deborah get there, the position of the paint brush in the sauce Doug has made changes between shots. (00:06:30)
Frozen Pop - S2-E15
Continuity mistake: Carrie says that her finger have broke off into her gloves. When she does, the ice scrapper in her hand changes hand instantly. (00:00:20)
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 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)
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)
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.