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)
Visible crew/equipment: Jessica asks Carrie what number they live at - as she does so a tape marker is visible on the floor. (00:06:50)
Continuity mistake: The first time Doug throws a ball at the bottles, we see one bottle remain lay down on the stand. Camera cuts and this bottle has disappeared. (00:18:00)
Continuity mistake: The guy on the stall puts 3 balls down in front of Doug in a line. Doug picks up the ball furthest from the guy. Camera cuts and now Doug has the ball closest to the guy. (00:17:30)
Soft Touch - S2-E22
Visible crew/equipment: When Doug and Carrie go to get up from having dinner with Saskies, tape markers are visible on the floor by their chairs. (00:05:30)
Frozen Pop - S2-E15
Continuity mistake: When Doug goes back into the house at the start he opens the door with his right hand. Camera cuts to inside the house and now it's his left hand on the door handle. (00:01:35)
Queasy Rider - S2-E1
Revealing mistake: We see Doug crash into the fridge 3 times, thus implying that it's 3 times he's crashed. However it is the same clip used for all 3 crashes. (00:13:40)
Queasy Rider - S2-E1
Visible crew/equipment: When Doug and Carrie are arguing over the bike a white tape marker can be seen on the floor. (00:09:20)
Continuity mistake: When Arthur's friend Mr. Glassman comes into the Heffernan house, a large tree can be seen on the front lawn, which we know from many other episodes there is not a large tree in front of the Heffernan house. (00:09:30)
Visible crew/equipment: When Doug is sitting in the living room and Carrie comes into the kitchen carrying groceries, a boom mic shadow is seen moving on the wall behind her. (00:04:10)
Frozen Pop - S2-E15
Continuity mistake: When Doug and Carrie wake up covered in sweat, the position and amount of blanket on Carrie changes just before she pushes the covers off and gets out of bed. (00:04:50)
Continuity mistake: In the exterior shot of Coopers there is a car parked, no bins, no people. However, in the immediate interior shot, you can see a garbage bin, newspaper box and people walking by in either direction. (00:13:15)
Continuity mistake: When Ritchi and Spence are at the cafe, Spence pours the remainder of the pitcher into his cup. The shot goes back to him, and it appears he took a large sip because his cup is near empty. When Doug and Deacon come in, Spence's glass is almost full again.
Continuity mistake: When Doug has just shot himself and Carrie calls him at work, he looks back to Deacon before answering the phone. On the platform behind Deacon, a woman IPS employee appears instantly. Also, the IPS staff walking behind them do not match between shots.
Continuity mistake: Doug and Carrie are fighting in the kitchen. Around the time that Carrie says, "I give you one thing and you screw it up," Carrie's handbag in the background is standing upright. The shot goes back to Doug. When it goes back to Carrie and she is leaving, she picks up her handbag which is now no longer upright. Her handbag also looks like it has been shifted.
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.