Queasy Rider - S2-E1
Revealing mistake: When Carrie and Doug are in the garage arguing about the bike, there is a shot of the fridge where tyre marks and a dent are visible. However we later see Doug make these marks. (00:09:00)
Queasy Rider - S2-E1
Revealing mistake: When Doug comes into the garage the first time, if you look through the garage door, at the end of the fence is a very noticeable crease running vertically. This shows the outside is a fake. (00:06:55)
Revealing mistake: When Arthur is looking in Carrie's bag, there is one shot with a blue kettle next to the bag. 10 stage lights can be seen reflected in the kettle. (00:11:50)
Queasy Rider - S2-E1
Continuity mistake: When Arthur is telling Carrie he has got a job, Carrie is putting out paper plates. She puts all three out and then the camera changes angle. When it does, one of the plates has moved across the table and Carrie is seen placing it in position again. (00:10:40)
Queasy Rider - S2-E1
Visible crew/equipment: When Doug is telling Carrie that he hates the bike, a crew member in blue jeans can be seen in the back of the mirror on the bike. (00:18:55)
Queasy Rider - S2-E1
Revealing mistake: When Doug comes in at the start and says he has been riding Ritchie's hog, all the stage lights can be seen in Carrie's wine glass. (00:02:20)
Queasy Rider - S2-E1
Other mistake: When Arthur is telling Doug that he had a bike, you can see and hear a bright light switch on in front of them.
Queasy Rider - S2-E1
Visible crew/equipment: When Doug is looking at the bike for the first time, all the stage lights are reflected in the helmets on the table. (00:06:00)
Continuity mistake: When Doug and Carrie are talking in the kitchen after Doug tried the Sgt. Salty cereal, you can see the cereal box disappear and then reappear on the table behind them. (00:12:45 - 00:13:35)
Continuity mistake: At the start when Carrie walks into the kitchen she opens the door with her right hand. However from the kitchen angle she is opening the door with her left hand and her right is down by her side. (00:03:10)
Continuity mistake: Right at the start, the salad cutlery keeps crossing and uncrossing itself. (00:01:05)
Factual error: At Shea Stadium, in Queens New York, Carrie asks Arthur if he want a Coolicoo. Carrie then goes to the concession to buy Coolicoo's and tells the guy behind the counter she can see them next to him. However, Coolicoos don't exist at Shea Stadium. They are only available at Dodgers Stadium in L.A.
Visible crew/equipment: When Doug and Arthur are eating in the buffet restaurant, stage lights are seen reflecting in the cup. Also, each time the camera goes from angle to angle, the cup has moved from one side of the table to the other, sometimes have a saucer, sometimes not. (00:06:35 - 00:08:20)
Soft Touch - S2-E22
Continuity mistake: Near the end when Carrie sits on the couch with Doug asking him about the water-filter business, her hand moves instantly from down by her side to on Doug's arm. (00:20:10)
Visible crew/equipment: When Carrie and Arthur pull into the driveway, the camera is reflected in the car. (00:18:15)
Visible crew/equipment: When Arthur is hinting it's his birthday soon, there is one shot where you can see the cupboards above the hatch into the kitchen. In this shot you can see a boom mic follow Arthur across the room. (00:02:30)
Soft Touch - S2-E22
Continuity mistake: When Doug is desperately trying to sell filters at IPS, he drops four boxes. When he picks them up, the position of one box in his right hand is constantly changing. Blue picture is facing the camera, but when the camera cuts, now Writting is facing where the camera was. Doug has not moved in this time. (00:17:55)
Soft Touch - S2-E22
Visible crew/equipment: When Doug gets into bed after arguing with his cousin, a camera shadow can be seen moving over the bed. (00:17:45)
Continuity mistake: At the buffet, the cup that is on the table is either on or off a saucer depending on the shot. (00:06:55)
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.