Wild Cards - S2-E20
Continuity mistake: When Doug calls Carrie to confess, note the phone cable. The loop changes between several shots from a neat loop to an extremely messy loop. (00:20:30)
Big Dougie - S2-E21
Revealing mistake: When Doug is jogging in the marathon he is casting three shadows in different directions. Also, the female jogger behind him appears to be in good shape but is still jogging as dramatically slow as Doug. (00:19:20)
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)
Soft Touch - S2-E22
Continuity mistake: At the start, when Carrie is trying to park, the same clip is shown. The same people walk by. (00:00:30)
Soft Touch - S2-E22
Continuity mistake: At the beginning, when Carrie is trying to park the car she's wearing a 3/4 sleeve blue top in the closeups, but in the overhead shot of the car for the last attempt when Carrie says that she's cutting it, the driver is not wearing that blue top, the driver is wearing a plaid shirt. (00:01:00)
Soft Touch - S2-E22
Revealing mistake: When Carrie is trying to park, the position of the shadows on the ground is changing drastically between shots. This cannot be attributed to it taking Carrie a long time to park, as the shadows move forward and back. (00:02:00)
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)
Soft Touch - S2-E22
Continuity mistake: When Carrie is asking Doug why he likes it at the neighbors, her arms are on her hips. Camera cuts and now they are straight down at her side. (00:08:40)
Soft Touch - S2-E22
Continuity mistake: When Doug and Carrie are arguing about selling filters, the bed covers keep changing place. Note the position in regard to the jeans. (00:09:05)
Soft Touch - S2-E22
Continuity mistake: When Doug is getting into bed while talking to Carrie about selling water filters, his grip on the duvet changes instantly. (00:10:00)
Soft Touch - S2-E22
Continuity mistake: When Doug is asking Carrie about the water, she puts a glass down and the level of water in both glasses is significantly different. Camera cuts and they are level. (00:11:10)
Soft Touch - S2-E22
Continuity mistake: When Doug is telling Arthur about the filters, there is a leaflet on the table. Between camera cuts, this leaflet is constantly changing position. (00:13:25)
Soft Touch - S2-E22
Continuity mistake: When Arthur is trying to get Mickey to take a sip of water, Mickey crosses his arms. When the shot changes back to Mickey, he crosses his arms again. (00:15:30)
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)
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
Continuity mistake: At the end when Carrie is telling Doug not to take any more shots, she has one hand on Doug's arm. Camera cuts and she now has two hands on his arm. (00:19:25)
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 says about going back in time, a boom shadow can be seen moving over the wall. (00:02:30)
Continuity mistake: When Doug and Deacon are talking about Doug wearing a disguise to the concession stand, There are two people on the loading bay holding a parcel. Camera cuts and this parcel is no longer in their hands. (00:13:00)
Continuity mistake: In the scene where Arthur is on the phone with PBS to complain about getting a "Civil War Series" box set, the actual set of tapes changes drastically. When it's on the table and when Carrie brings it over to the counter its a pretty large, has an American flag motif, and says "Civil War" across the top. When it cuts back to it sitting on the counter its a much smaller box with a plain design and says "The Great War" along the bottom. It's obviously a different set, not just the camera angle. (00:14:40)
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.