Continuity mistake: At the start Doug puts a drink down after taking the top off. Camera cuts and the lid is back on. (00:03:30)
Continuity mistake: When Doug first enters the gym, you can see a price tag hanging off of the front of his weight belt. In the shots following this, the price tag is gone. (00:11:10)
Continuity mistake: The Saskeys are Doug's neighbors in this episode despite them having moved away back in the season 2 episode "Soft Touch" (00:02:30)
Continuity mistake: When we first see Doug at the gym, the sweat stains on his shirt keep changing size. (00:11:30)
Revealing mistake: When Doug runs into the phone when trying to deliver Carrie's package, it's very clear he doesn't touch the phone with his head.
Strike One - S3-E5
Visible crew/equipment: After Carrie discovers she can't take a shower because Doug ripped out the shower tiles, when she walks out of the bathroom keep your eye on the window at the right. Just as Doug lifts the hammer a crew member is visible in the bathroom's window (it's not Doug's reflection). (00:17:15)
Continuity mistake: After throwing the dummy out the door, Doug kicks his bag out the door too, only for it to reappear a few minutes later. (00:18:20)
Continuity mistake: Doug throws the dummy out the front door and in doing so, knocks a green Jets jacket to the floor. In the next shot the jacket is back on the stand. (00:18:40)
Hi Def-Jam - S3-E13
Other mistake: When playing poker, Stef says she has all hearts which is a flush. However if you look at the cards she puts on the table, there is a 6 of diamonds and 3 of clubs. Therefore, not a flush. Everyone at the table, (Lou, Mr. Prezants, Deacon, Spencer and Doug) all agree it's a flush. (00:13:30)
Continuity mistake: At the beginning during dinner, Carrie hands Doug the salad bowl, then puts the spoon into the bowl and hands it to him again in the next shot. (00:02:25)
Factual error: In this episode Doug is denied getting a better route when it's given to the new guy because he's "better looking." As member of a union, Doug most certainly would have been given precedent over any new driver.
Visible crew/equipment: When Carrie come out into the back garden to speak to Doug and Deacon, a boom mic drops into shot very briefly. (00:08:55)
Strike Out - S3-E7
Continuity mistake: When Arthur sits down for his meal, there is a bottle on the table. The lid is either on or off depending on the shot. (00:03:30)
Strike One - S3-E5
Visible crew/equipment: When Spence's taxi pulls away, a crew member, light screen and stage light can be seen reflected on the window of the taxi. (00:18:10)
Continuity mistake: When Carrie asks Arthur how a legless dummy will protect her on the subway, her arms are either on the table or off, depending on the shot. (00:10:30)
Hi Def-Jam - S3-E13
Visible crew/equipment: When Mr. Purzan finds out that Stephanie doesn't want to date him and runs off like a little nancy-boy, we see his reflection pass through the picture in the hall. A moment later we can see the reflection of two people pass in the opposite direction but no one walks back into the room. (00:20:30)
Strike Out - S3-E7
Continuity mistake: After Doug says "Let's hit the streets", Doug, Arthur, Deacon and Kirby go on a mini crime-spree. During this montage each characters outfit completely changes several times. They are also dressed very lightly for late October/early November in New York. (00:13:00 - 00:14:00)
Strike One - S3-E5
Continuity mistake: When Doug has a look at the bumper sticker Spence has, there is one fold in it, but when it cuts there is now three. (00:14:40)
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.