Continuity mistake: At the start, when Carrie is talking to Arthur about being inseparable she has her jacket over her arm. Camera cuts and now she is putting it on instantly. (00:00:10)
Continuity mistake: When Carrie takes a drink from her cup of tea she is holding her cup with 1 hand in one shot and 2 in a second shot. (00:14:30)
Queasy Rider - S2-E1
Continuity mistake: As Doug is telling Carrie he hates the bike, his beer and crisps vanish instantly from the sofa. (00:19:20)
Strike Out - S3-E7
Continuity mistake: After Doug says "Let's hit the streets", Doug, Arthur, Deacon and Kirby go on a mini crime-spree. During this montage each characters outfit completely changes several times. They are also dressed very lightly for late October/early November in New York. (00:13:00 - 00:14:00)
Continuity mistake: During the first shuffleboard scene, the characters are brightly lit and cast by long dark shadows (indicating early morning or late afternoon), but when you see shots of the shuffle pucks flying into the bleachers, the bleachers' and extras' shadows are cast straight down (indicating noon hour).
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.
Dire Strayts - S2-E8
Continuity mistake: When Doug is talking to Ray at the table, the position of his beer changes between shots. Watch the label. (00:02:45)
Dire Strayts - S2-E8
Continuity mistake: When Doug talks about grown men not being able to watch the game, the amount of head on his beer changes instantly. (00:02:40)
Queasy Rider - S2-E1
Continuity mistake: When Doug starts to explain to Carrie about getting the bike, he has his hands on the edge of the back of the chair. Camera cuts and now they have moved close together in the middle of the chair. (00:07:55)
Continuity mistake: During both driving scenes, the street lights in the background do not fade away in the distance to indicate they are actually driving forward. When Doug, Carrie and Arthur are pulled over waiting for Spence (and again when waiting for Arthur at Dairy Queen), lights scroll over the car and the sound of a passing vehicle can be heard but no car is seen to pass by or drive away in the distance. (00:07:45)
Strike One - S3-E5
Continuity mistake: When Doug has a look at the bumper sticker Spence has, there is one fold in it, but when it cuts there is now three. (00:14:40)
Continuity mistake: In the episode where Priority Plus is mentioned, after the Priority Plus driver has got Doug Out of the drive through, he gives Doug a lift in his truck. In some shots there is a window on the side of the street. In the window there is no Priority Plus truck visible.
Continuity mistake: When Doug says that there is nothing going on at work, his hands are flat on the table, camera cuts and he's got one up in the air. (00:06:50)
Continuity mistake: From outside shots of Coopers, there are no garbage bins or newspaper boxes in front of the pub. From inside shots, several bins can be seen just outside the glass doors.
Inner Tube - S3-E17
Continuity mistake: When Arthur brings the tray to Doug in bed, the position of the duvet/sheet is constantly changing. (00:06:20)
Strike Out - S3-E7
Continuity mistake: When Carrie and Kelly are setting the table, Kelly is handing plates to Carrie. She hands Carrie a plate and has one left in her hands. The camera cuts, and she now has two plates in her hand. (00:06:20)
Strike Too - S3-E6
Continuity mistake: At the end, when Carrie talks about going upstairs, she has her hand on Doug's arm on the back of the sofa. When the shot changes, it's now lying in front of her. (00:20:20)
Continuity mistake: The lady walks away from Carrie's desk with some flowers. When she does, there are three petals on Carrie's desk which disappear without being touched. (00:06:10)
Strike Too - S3-E6
Continuity mistake: The writing on the blackboard changes between shots when Doug writes his name. Note the R in Mr. (00:15:10)
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.