Hungry Man - S1-E21
Continuity mistake: At the start Arthur goes from cutting bananas to having his hands on the side in between instant cuts. (00:01:10)
Train Wreck - S1-E20
Continuity mistake: When Arthur is rewriting his epitaph, the pad and pencil keep moving between shots. (00:12:10)
Train Wreck - S1-E20
Continuity mistake: When Julie goes to get her jacket, Doug's board swaps hands instantly. (00:03:40)
Continuity mistake: At the end, the shawl around Carrie's shoulder is either covering her shoulder or not depending on the shot. (00:20:50)
Visible crew/equipment: When Carrie asks Doug to go and check out the smell in the basement, there are tape markers visible by the fridge. (00:05:20)
Continuity mistake: When Carrie starts praying in the bedroom, Doug has his hands together. Camera changes and he has got his watch in his hands. A watch that was not in his hands or on his wrist before, might I add. (00:09:50)
Window Pain - S5-E2
Continuity mistake: When Carrie and Doug are having the discussion about the dry cleaning, the way Carrie is holding it changes instantly. (00:06:10)
Continuity mistake: When Arthur sits down to talk about the deodorant with Doug, Doug's hand is flat on the table. Camera changes and it's now on the doughnut box. (00:11:00)
Continuity mistake: When Arthur is talking to Doug in the hospital, the pillow behind Arthur keeps changing position. (00:11:00)
Other mistake: When Doug is saying that Arthur does nothing that Deacon just listed, there is a camera angle of him walking down the aisle with Deacon. In this camera angle only there is a blip to the top right of the screen. This little black mark stays in shot while the camera is moving and is only in this one angle. In other shots of the same angle the black mark is not present. Clearly something was on the camera lens during filming. (00:05:30)
Revealing mistake: When the screen says "2 months later" the camera shakes. (00:21:20)
Continuity mistake: When the doctor is explaining to Carrie what is wrong with Arthur, he has a stethoscope round his neck that keeps changing position between shots. (00:08:30)
Continuity mistake: When talking about getting a pumpkin, Deacon knocks a toy onto the floor, When the camera moves back you can see the toy has gone. (00:01:30)
Visible crew/equipment: When Doug is outside talking to Deacon and Arthur opens the kitchen door, as the door swings back you can see all the set lights reflected in the glass. (00:08:20)
Continuity mistake: When Kelly says to Deacon "Maybe it's 'cause you're walking late all the time" she has her mug up in the air, camera cuts and it's down on the table. (00:06:25)
Continuity mistake: When Arthur walks into the kitchen at the start and picks up the phone, the door is closing. The camera cuts to Doug at IPS, then back to Arthur and the door is still at the same point of closing. (00:00:55)
Revealing mistake: During the scene when Doug is "out with the boys" driving in Spence's car, you can tell they are actually in a studio using a green-screen because the stage lights reflecting off the car don't move. (00:36:00 - 00:36:35)
Other mistake: When Doug and Carrie go to visit the new neighbour, Jessica, Carrie tells her that they live at #8013; however many other episodes we see the numbers 3121 on the Heffernan's door and later learn that the Heffernan's live at 3121 Aberdeen Street in Rego Park. (00:28:35 - 00:29:35)
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.