Visible crew/equipment: When Doug and Carrie leave for their holiday, a stage light is reflected on the kitchen door. (00:09:30)
Factual error: Doug goes to the doctor for a check up after losing some weight. They live in New York, but the address on the outdoor sign is actually in California. (23101 Sherman Pl).
Continuity mistake: At the start, the distance the canoe has drifted changes instantly. And it changes a huge distance. (00:04:20)
Factual error: It is very obvious throughout the whole episode that the mountain scenery is that of California wilderness...the trees, plants and mountains look nothing like those in New York or the East Coast.
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)
Revealing mistake: When Doug snaps his bat it's very clear it is pre-broken. (Possibly from a previous take or to make it easier for Kevin James.) (00:07:55)
Visible crew/equipment: At the end of the episode when Carrie and Doug are arguing about her letting him win a ping pong game, all the windows over the bed are closed, they leave the bedroom to go play a rematch, when they return to the bedroom Carrie starts pushing Doug down on the bed and the middle window is open, as they lay down further you can see someone swing the window shut. (00:27:00 - 00:28:00)
Revealing mistake: In the final scene, Carrie starts to kiss Doug and pushes him onto the bed. The camera angle switches from what would be outside the window to beside the bed. The scene was done in one take from 3 camera angles. As the camera pans left you can see the center window is completely open because they had just pulled the camera out of it and didn't get it closed yet, and you can watch the window be closed by an invisible hand from underneath. (00:28:00)
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.
Continuity mistake: In the scene where Spence is entering the place his girlfriend works, he is pushing the door in. When the camera angle switches he is pulling the door open.
Continuity mistake: Carrie says that Deacon does not "drink or smoke." Previous episodes have shown him drinking beer with the guys. Also, in the episode "Friender Bender", it was mentioned that he drank a margarita during dinner at a restaurant.
Continuity mistake: Doug goes to Deacon's to tell him about Kelly wanting to get back together. Deacon is putting on his shoes and in different shots, sometimes his shoe is almost on and then other shots it shows him holding it in his hand about to put it on again.
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.