Continuity mistake: The way Carrie is standing and holding the banana and pop-tart changes as Doug admits that he was trying to look into the strip club, not reaching for a Fig Newton. (00:15:15)
Continuity mistake: After Spence and Kirby's arm wrestle, the way Spence holds the action figure keeps changing between shots. (00:51:10 - 00:51:55)
Continuity mistake: When Kirby says that Spence is scared of peanuts and calls him "The Scaredinator", his hands are empty and his arms are folded - then in the next shot he is instantly holding the red action figure again. (00:51:40)
Continuity mistake: When Arthur's friend Mr. Glassman comes into the Heffernan house, a large tree can be seen on the front lawn, which we know from many other episodes there is not a large tree in front of the Heffernan house. (00:09:30)
Continuity mistake: At the dinner table while talking about being obscure at work, Doug starts pouring his beer into a glass. But immediately in the next shot he is finished pouring and both bottle and glass are on the table. A moment later he picks up the beer and pours it into the glass a second time. (00:03:45)
Affair Trade - S9-E2
Continuity mistake: When Doug and Jessica run into Carrie in the parking lot at the Dr. Heffernan office, there is a man walking up from behind them with grey hair. In the next shot he instantly appears beside them unrealistically fast. (00:19:20)
Frozen Pop - S2-E15
Continuity mistake: When Doug and Carrie wake up covered in sweat, the position and amount of blanket on Carrie changes just before she pushes the covers off and gets out of bed. (00:04:50)
Continuity mistake: In the exterior shot of Coopers there is a car parked, no bins, no people. However, in the immediate interior shot, you can see a garbage bin, newspaper box and people walking by in either direction. (00:13:15)
Continuity mistake: When Ritchi and Spence are at the cafe, Spence pours the remainder of the pitcher into his cup. The shot goes back to him, and it appears he took a large sip because his cup is near empty. When Doug and Deacon come in, Spence's glass is almost full again.
Continuity mistake: When Doug has just shot himself and Carrie calls him at work, he looks back to Deacon before answering the phone. On the platform behind Deacon, a woman IPS employee appears instantly. Also, the IPS staff walking behind them do not match between shots.
Continuity mistake: Doug and Carrie are fighting in the kitchen. Around the time that Carrie says, "I give you one thing and you screw it up," Carrie's handbag in the background is standing upright. The shot goes back to Doug. When it goes back to Carrie and she is leaving, she picks up her handbag which is now no longer upright. Her handbag also looks like it has been shifted.
Frozen Pop - S2-E15
Continuity mistake: When Doug has just gone back to bed and Arthur walks in, Doug's position on the bed changes instantly. He swaps sides. (00:05:35)
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)
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.