Revealing mistake: When Doug tells Arthur his toast is done, there is no smoke, but as soon as he is finished speaking there is smoke coming from the toaster. (00:04:05)
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: Deacon says "How do we know cutie-pie isn't cutie-guy?" then crosses his arms. In the next shot his arms are immediately uncrossed and on his hips when Doug replies. (00:06:00)
Taste Buds - S5-E24
Other mistake: When Doug sits down to eat and Arthur touches his food, Doug says, "That's what my sandwich was missing, a finger with a loose bandaid on it," and pushes Arthur's hand away. When he does this you can see Arthur isn't wearing any bandaids on his hands. (00:00:05 - 00:01:00)
No Retreat - S4-E5
Other mistake: In the opening scene when Doug is cooking hotdogs for his friends, the smoke coming from the BBQ is very fake. (00:00:20)
Other mistake: At the end when Doug takes the bandages off Carrie's face, the bandages come off far too easily as if they weren't really attached in the first place.
Revealing mistake: When Doug stops to tie his shoe outside the car dealership and Carrie walks up to grab him, you can see the fake back-drop sway with her motion. (00:08:35)
Dog Shelter - S5-E23
Visible crew/equipment: When Doug finds out that Rocky is in fact Rocky 4, a boom mic is reflected in the window. (00:10:20)
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.