Taste Buds - S5-E24
Continuity mistake: Just after Carrie tells Doug that she knows what he has been doing, she storms out of the kitchen. Doug has his hand on a water bottle on the table, then picks it up as he rushes after Carrie. In the next shot of Doug walking into the living room, the water bottle is gone.
Revealing mistake: When driving the Mini, the reflection on the bonnet never changes despite being on the highway. (00:12:00)
Fixer Upper - S1-E12
Continuity mistake: At the start, the items in Carrie's hands swap hands instantly. (00:00:10)
Visible crew/equipment: When Richie is explaining about getting rid of the car, tape markers are visible by Doug's feet. (00:14:40)
Visible crew/equipment: After the first drive in the Mini, a stage light is reflected clear as day in the bonnet. (00:13:20)
Continuity mistake: When the guy chucks his cheque book into the basket, it reappears in his hand a second later. (00:11:20)
Revealing mistake: As Carrie skids into the parking spot at the start, skid marks are visible on the floor from previous takes. (00:00:30)
Road Rayge - S1-E9
Audio problem: Doug gets his license back and gets into his car. We hear the engine start, but his hands are seen on screen at the time. (00:20:00)
Road Rayge - S1-E9
Continuity mistake: When driving Doug home, look out the back window to see 2 red car lights appear instantly and out of nowhere. (00:12:20)
Road Rayge - S1-E9
Visible crew/equipment: As Doug takes Ray's keys, the film crew and equipment are reflected in the wing mirror. (00:09:50)
Road Rayge - S1-E9
Continuity mistake: When trying to get Doug to drive after the Jets' game, Ray's press pass goes from white to green instantly. (00:09:20)
Visible crew/equipment: When speaking to Doug about the book, a crew member is reflected in the window. (00:19:35)
Continuity mistake: In the first classroom scene there are two people sat to Doug's right. These people then vanish a few seconds later. (00:07:55)
Head First - S1-E6
Audio problem: Doug calls Arthur near the start and the audio is overdubbed. (00:03:15)
Visible crew/equipment: At the start when Carrie says says "it's already 20 of" look at the screen right to see the kitchen cabinets swing into place as the crew replace them. (00:00:35)
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.