Continuity mistake: When Doug Tells Carrie to pack for Atlantic City the cushion is either on or off her lap. (00:17:15)
Visible crew/equipment: Doug calls the phone number of the mystery guy, and when mystery guy answers his cell just a few feet away from Doug, two green tape marks are visible on the floor near Doug's feet. (00:16:30)
Frozen Pop - S2-E15
Visible crew/equipment: While Doug is scraping the windshield in the wide shots, the end of the street backdrop and production equipment are visible at the upper left side of the screen. (00:01:15)
Visible crew/equipment: Doug whisks Carrie to the boardwalk straight from the train after work, and when Doug points to the booth with plush frogs, a camera is visible on the left side of the screen as it moves out of shot. (00:17:20)
Train Wreck - S1-E20
Visible crew/equipment: At IPS, while Doug gives his speech about using heavy package stickers, in the shots facing the drivers seated at the table, the end of the IPS set and a crew member are visible at the right side of the screen. (00:08:45)
Revealing mistake: At the start, when Arthur returns the book to Carrie then asks if she'd like to jot down his musings, we can see through the back door's window, and the backyard set's foliage pattern wallpaper is falling off the backdrop. It's visible later as well. (00:02:45)
Revealing mistake: After Doug successfully trades vacation days with Roger, it cuts to Doug's IPS truck stopping in traffic. The next few shots were filmed on the streets at Sony Pictures Studios lot. In the shot of the IPS truck's side-view mirror (as the RV approaches), note the signs on the building read "Keaton Building" and "Sound Department Courtyard." After the flashback, another building sign reads "Durante Building." These buildings are located at the north side of the studio in Culver City, CA. (00:03:20)
Visible crew/equipment: During the flashback, while Doug is waiting on the porch Carrie rushes out then gets into her car to take off, and in the next shot facing the front door, the reflections of the camera operator, wearing a white baseball cap, and the camera are visible on the window. (00:12:35)
Visible crew/equipment: During the flashback, when Carrie walks over to Doug at the side of the house, and he zips himself up, in shots facing Doug, a crew member and production equipment are visible on the right side of the screen. (00:20:10)
Soft Touch - S2-E22
Visible crew/equipment: At the start, in the shots facing Carrie and Doug while they're in the car, we can see a screen atop the roof on the driver's side of the car with its reflection on the windshield (and its shadow on the car's hood). This is gone in the overhead long shots. (00:00:10)
Continuity mistake: When Doug puts down the remote to grab Carrie's Walkman, the position of the remote changes between shots. (00:00:45)
Food Fight - S4-E13
Continuity mistake: When Arthur tells Doug to eat some salad he is either holding the bowl or not depending on the shot. (00:18:40)
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: Doug gets into a mess with the sellotape wrapping Carrie's Christmas present. However when she walks downstairs it's on the table, absolutely fine. (00:02:20)
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.