Visible crew/equipment: At the end in the theatre, a boom mic drops into shot. (00:19:00)
Visible crew/equipment: At the start when Carrie says says "it's already 20 of" look at the screen right to see the kitchen cabinets swing into place as the crew replace them. (00:00:35)
Visible crew/equipment: When Spence is leaving after dropping off the pictures a stage light is reflected in the door. (00:08:50)
Visible crew/equipment: After Spence gets weird while taking pictures of Sara at the anniversary party, when it cuts to the wide shot as Arthur says, "Okay, Garver!" a camera is visible at the right side of the screen.
Visible crew/equipment: At the start, while Doug and Carrie are in the jewelry store, in the shot of Doug swinging the shopping bags at the overhead surveillance camera, we can see a production camera at the left side of the screen. Then in the next shot, from the POV of the surveillance camera, the edge of the store's set is visible at the right side of the screen. (00:02:05)
Visible crew/equipment: During the driving scene at 00:07:35 you can see a stage wall on the set to the right when the lights pass over the car. (00:07:35)
Visible crew/equipment: When speaking to Doug about the book, a crew member is reflected in the window. (00:19:35)
Road Rayge - S1-E9
Visible crew/equipment: When Doug's paper gets ripped up, look at Ray and Doug's feet. A blue and white tape marker is visible by each of them. (00:06:10)
Road Rayge - S1-E9
Visible crew/equipment: As Doug takes Ray's keys, the film crew and equipment are reflected in the wing mirror. (00:09:50)
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)
Visible crew/equipment: When Arthur is talking about the store clerk hiding yam's out the back, there is an orange marker on the floor between the two men. (00:14:20)
Visible crew/equipment: When the store clerk walks off from talking to Arthur an orange T marker is visible where he was stood. (00:14:50)
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 the first drive in the Mini, a stage light is reflected clear as day in the bonnet. (00:13:20)
Visible crew/equipment: When Richie is explaining about getting rid of the car, tape markers are visible by Doug's feet. (00:14:40)
Visible crew/equipment: While Doug and Carrie are in the kitchen talking about Doug's job, right after Carrie says, "Wait him out 5 or 10 years," in the next shot facing the sink, we can see the end of the kitchen set at the right side of the screen. (00:14:00)
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.