Continuity mistake: When Carrie takes the first lot of Hofferman's pictures off Doug, she's holding them portrait. Camera cuts and she's holding them landscape. (00:05:30)
Continuity mistake: The leaflet in Carrie's hand at the start vanishes instantly. (00:03:10)
Continuity mistake: When Carrie is on about having never spent that much on a vacation, she has a leaflet in her hand that is open. Camera cuts and now it is partially closed. (00:03:10)
Continuity mistake: When Doug is being a polar bear, the bag Carrie was looking in disappears. (00:08:00)
Continuity mistake: When Doug asks Carrie to take a photo of him on the bed, there is nothing on the bed. After she says "stop", 2 items have appeared on the bed that were not in the previous shot. (00:08:45)
Continuity mistake: When Tim asks Doug if he wants to tee off back at the start of the hole rather than halfway down the fairway, he is pointing with his golf club. Camera cuts and he isn't. (00:15:35)
Continuity mistake: When the Marshall is chasing after Doug the distance between the two changes drastically. (00:16:00)
Continuity mistake: When Doug and Carrie are told that mold isn't covered by their insurance, Doug has his fist clenched by his mouth. Camera cuts and now it's open palmed and on the side of his head. (00:01:00)
Continuity mistake: When Arthur and Spence are talking in the kitchen, a fork keeps appearing and disappearing from Spencer's plate. (00:05:40)
Continuity mistake: When Doug and Carrie are talking about the fact the workmen have actually turned up, the cup on the table keeps rotating with no-one touching it. (00:12:15)
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)
Taste Buds - S5-E24
Continuity mistake: Just after Carrie tells Doug that she knows what he has been doing, she storms out of the kitchen. Doug has his hand on a water bottle on the table, then picks it up as he rushes after Carrie. In the next shot of Doug walking into the living room, the water bottle is gone.
Continuity mistake: At the start, the distance the canoe has drifted changes instantly. And it changes a huge distance. (00:04:20)
Continuity mistake: When Arthur asks Doug for a game of ping pong, the paddle is lying flat on the table. In the next shot there is a ball under the paddle which Arthur picks up (The ball is still on the table). In the next shot the paddle is back on the table and the ball is missing. (00:03:15)
Continuity mistake: When Arthur asks Doug for a game of ping pong, a ball suddenly appears under his bat and then disappears and Doug throws him the ball to have the first serve.
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.