Frozen Pop - S2-E15
Continuity mistake: When Carrie is telling Arthur to move upstairs, the blanket Arthur has got changes position instantly. (00:02:40)
Continuity mistake: At the beginning Carrie is dishing out potatoes from a bowl with a large black spoon, and as the camera changes angles her arm has not moved and she is now holding a small fork getting chicken from a different bowl. (00:01:40)
Continuity mistake: When Arthur asks Doug for a game of ping pong, the paddle is lying flat on the table. In the next shot there is a ball under the paddle which Arthur picks up (The ball is still on the table). In the next shot the paddle is back on the table and the ball is missing. (00:03:15)
Revealing mistake: When Doug snaps his bat it's very clear it is pre-broken. (Possibly from a previous take or to make it easier for Kevin James.) (00:07:55)
Visible crew/equipment: When Carrie walks in and sees Hollie for the first time in the episode, a boom mic can be seen following Carrie across the kitchen. (00:07:00)
Continuity mistake: The second time we see Doug's disk, it is spinning. In one shot it is spinning in shadow, but in the second shot it is in the sunlight. (00:08:00)
Visible crew/equipment: When we see Arthur playing Shuttleboard for the first time, his mic pack is visible. (00:08:00)
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.