Soft Touch - S2-E22
Continuity mistake: Near the end when Carrie sits on the couch with Doug asking him about the water-filter business, her hand moves instantly from down by her side to on Doug's arm. (00:20:10)
Silent Mite - S7-E7
Continuity mistake: In the final scene where Arthur takes his ornament from near the bottom of the tree and puts it closer to the top, the door to the kitchen is closed. Then in the next shot from inside the kitchen, the door is already open as Arthur walks towards camera. (00:21:15)
Soft Touch - S2-E22
Continuity mistake: When Doug is desperately trying to sell filters at IPS, he drops four boxes. When he picks them up, the position of one box in his right hand is constantly changing. Blue picture is facing the camera, but when the camera cuts, now Writting is facing where the camera was. Doug has not moved in this time. (00:17:55)
Continuity mistake: At the buffet, the cup that is on the table is either on or off a saucer depending on the shot. (00:06:55)
Continuity mistake: When Doug and Arthur sit down to eat, the cup that is on the table is either by Arthur or by Doug depending on the shot. (00:06:35)
Continuity mistake: When Arthur walks in near the start, Carrie is looking at him. Camera cuts and she is now looking in the totally opposite direction.
Continuity mistake: After Doug has shot himself, the position of the staple gun on the bench keeps changing without anyone touching it. (00:06:40)
Continuity mistake: After trying the Sgt. Salty cereal, while talking to Carrie, Doug gets out a plate to make something else to eat. After he puts the plate down on the table, the cereal box moves and switches sides. (00:13:30)
Cheap Saks - S6-E15
Continuity mistake: At the art gallery, the way Doug is holding the program instantly changes a couple times; arms crossed/uncrossed, program folded/unfolded. (00:02:20)
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)
Continuity mistake: When Doug goes to meet up with Ray, Richie zips up his jacket. In the next shot his jacket is unzipped. (00:06:20)
Continuity mistake: In episodes that show the outside of the IPS building, there are some shots that show a pay phone outside of the building, then other shots where the pay phone is missing.
Continuity mistake: The door to the house is on a corner. However, in the interior shots, they have a window each side of the door.
Continuity mistake: When Carrie says that Doug is losing brain cells in the garage due to fumes, the way she holds the tickets changes instantly. (00:12:20)
Continuity mistake: Carrie and Arthur are talking about Carrie making a Thanksgiving meal, and as they are talking the frozen meals in Carrie's trolley change position between shots. (00:03:10)
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.