Revealing mistake: While Doug and Carrie are heading home after game night at the Palmers, they pass the street sign for Buena Vista St, twice, as they're driving up Magnolia Blvd in Burbank, CA.
Revealing mistake: When Carrie holds the paper towels, the kitchen's curtains over the sink are normal, the window is closed and the blinds are down. However, next shot the blinds are up, the double-hung window is oddly open outward sideways, and the curtain is pulled back with a large clamp. Then it's all back to the normal previous way.
Visible crew/equipment: Doug calls the phone number of the mystery guy, and when mystery guy answers his cell just a few feet away from Doug, two green tape marks are visible on the floor near Doug's feet. (00:16:30)
Visible crew/equipment: While Doug, Carrie, and Arthur are on the checkout line, Doug notices the mystery guy on another line, and two tape marks (an orange and a green) are visible on the floor near Doug's shopping cart. (00:20:20)
Visible crew/equipment: After Arthur coerces Carrie into inviting quite a few others to their dinner she reminds him of his inside voice, then, when Arthur walks away to get the gherkins in aisle 4, there are multiple visible T-marks taped to the floor behind Carrie. (00:07:05)
Continuity mistake: In the first shot inside Arthur's house, Carrie and Doug are standing together when Carrie mentions how tough it must be for Arthur. It then cuts to Arthur sitting at the table, with Doug right there sitting beside Arthur. Next shot Doug is still standing with Carrie as she urges Doug to spend some time with Arthur, so this is when Doug walks over to his father-in-law. (00:07:00)
Audio problem: While all four guys are on the bed watching the game, Richie's eating a sub so we hear Doug say, "Hey, Richie, come on," but Doug's lips are closed and not moving in this shot. (00:15:10)
Revealing mistake: While Doug is driving the IPS truck he stops in traffic, and then Arthur pulls up alongside. Watch the reflection in the truck's side mirror, because we can see crew members pushing Arthur's car as he takes off. (00:19:10)
Train Wreck - S1-E20
Revealing mistake: Shari from ISP radios Doug about the rush order pickup at 1202 Stratford, so Doug pulls over and soon Carrie pulls him to the back of the truck. Cut to exterior shot of the truck, and the street sign reads "Lafayette, Culver City" which reveals the California location. The truck is parked on Culver Blvd, corner of Lafayette, in front of the well known Washington Building (awnings are now black), which is located a few blocks up from Sony Pictures Studios where King of Queens was filmed. (00:21:35)
Train Wreck - S1-E20
Visible crew/equipment: At IPS, while Doug gives his speech about using heavy package stickers, in the shots facing the drivers seated at the table, the end of the IPS set and a crew member are visible at the right side of the screen. (00:08:45)
Train Wreck - S1-E20
Continuity mistake: When Doug sees Arthur's headstone in the yard, the dark opaque flap of the dog door is missing from its frame, but it reappears as Doug enters the kitchen. (00:06:40)
Train Wreck - S1-E20
Visible crew/equipment: When Arthur asks Doug for help with the epitaph, the green and red tape markers are visible on the floor in front of the dishwasher, where Doug stands. (00:12:00)
Visible crew/equipment: Doug whisks Carrie to the boardwalk straight from the train after work, and when Doug points to the booth with plush frogs, a camera is visible on the left side of the screen as it moves out of shot. (00:17:20)
Visible crew/equipment: When Doug uses the ridiculous RV horn and startles Carrie awake, as she walks from the sofa to the front door, the overhead studio lights are visible at the top of the screen. (00:11:40)
Revealing mistake: After Doug successfully trades vacation days with Roger, it cuts to Doug's IPS truck stopping in traffic. The next few shots were filmed on the streets at Sony Pictures Studios lot. In the shot of the IPS truck's side-view mirror (as the RV approaches), note the signs on the building read "Keaton Building" and "Sound Department Courtyard." After the flashback, another building sign reads "Durante Building." These buildings are located at the north side of the studio in Culver City, CA. (00:03:20)
Revealing mistake: At the start, when Arthur returns the book to Carrie then asks if she'd like to jot down his musings, we can see through the back door's window, and the backyard set's foliage pattern wallpaper is falling off the backdrop. It's visible later as well. (00:02:45)
Strike One - S3-E5
Revealing mistake: In the kitchen, when Doug tells Carrie he knows the strike will end in 1 or 2 weeks tops because he's a Union Member, the blue shelves/cabinet on the wall behind Doug are positioned properly. Then, when Carrie asks him what the strike issues are, watch as the blue shelves move sideways behind Doug (this wall with blue shelves/cabinet is hinged to provide camera access). (00:13:00)
Strike One - S3-E5
Visible crew/equipment: When it cuts from Doug singing with the barbershop quartet, to Doug and Carrie standing in the garage with the new vehicle, the end of the garage set wall is visible on the left side of the screen. (00:09:35)
Visible crew/equipment: During the flashback, when Carrie walks over to Doug at the side of the house, and he zips himself up, in shots facing Doug, a crew member and production equipment are visible on the right side of the screen. (00:20:10)
Visible crew/equipment: During the flashback, while Doug is waiting on the porch Carrie rushes out then gets into her car to take off, and in the next shot facing the front door, the reflections of the camera operator, wearing a white baseball cap, and the camera are visible on the window. (00:12:35)
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.