No Orleans - S4-E16
Continuity mistake: Doug made a blue snowcone in the kitchen and then goes into the living room to talk to Arthur. When he crosses the door in to the living room, the initially full snow cone is now almost gone. (00:02:05)
Visible crew/equipment: When Doug and his friends are moving the TV back downstairs, in the first shot just as Spence announces his finger is getting crushed, a camera operator with camera are visible on the left side of the screen. (00:12:45)
Continuity mistake: Arthur and Doug are sitting with beers in the basement. Arthur doesn't open his beer, but the sound of a bottle opening can be heard and suddenly his beer has foam all the way up to the top of the bottle. Arthur stands up and the bottle is still unopened. It cuts to Doug, then back to Arthur with no beer at all. Again it cuts to Doug, then back to Arthur, and he is holding the unopened beer again. (00:18:30)
Fixer Upper - S1-E12
Continuity mistake: Doug finishes playing the tennis game on the TV with Arthur and goes into the kitchen to get the Cheese Doodles. While talking to Carrie, he puts the Cheese Doodle package on the table with a can of cola behind it. He then goes to get a glass from the cupboard and in the next shot you see the cola is in front of the Cheese Doodles. (00:17:30)
Visible crew/equipment: During the driving scene at 00:07:35 you can see a stage wall on the set to the right when the lights pass over the car. (00:07:35)
Continuity mistake: When Spence and Kirby are talking about why Spence can't make him a PB&J sandwich, the way Kirby holds the red action figure keeps changing. (00:06:15 - 00:06:55)
Continuity mistake: In the overhead shot when Carrie parks there is no-one around. From the internal shot, there are 2 people visible through the side windows. (00:00:40)
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)
Revealing mistake: When we see the montage of Doug working as a manager, in one overhead shot you can see the image on the PC is simply stuck on to make it seem like it's on. (00:08:50)
Revealing mistake: Even after receiving the gift basket from the neighbors, the Heffernans are still awakened by their barking dog. When Carrie rushes downstairs Doug stops her at the front door, and the entire left window has been removed (for camera access) from its frame, so there's a large empty hole. (00:13:10)
Visible crew/equipment: While Doug and Carrie are in the kitchen talking about Doug's job, right after Carrie says, "Wait him out 5 or 10 years," in the next shot facing the sink, we can see the end of the kitchen set at the right side of the screen. (00:14:00)
Strike One - S3-E5
Visible crew/equipment: After Carrie discovers she can't take a shower because Doug ripped out the shower tiles, when she walks out of the bathroom keep your eye on the window at the right. Just as Doug lifts the hammer a crew member is visible in the bathroom's window (it's not Doug's reflection). (00:17:15)
Visible crew/equipment: At the start, while Doug and Carrie are in the jewelry store, in the shot of Doug swinging the shopping bags at the overhead surveillance camera, we can see a production camera at the left side of the screen. Then in the next shot, from the POV of the surveillance camera, the edge of the store's set is visible at the right side of the screen. (00:02:05)
Continuity mistake: When Carrie is on about having never spent that much on a vacation, she has a leaflet in her hand that is open. Camera cuts and now it is partially closed. (00:03:10)
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.