Continuity mistake: In the scene where Spence is entering the place his girlfriend works, he is pushing the door in. When the camera angle switches he is pulling the door open.
Continuity mistake: Carrie says that Deacon does not "drink or smoke." Previous episodes have shown him drinking beer with the guys. Also, in the episode "Friender Bender", it was mentioned that he drank a margarita during dinner at a restaurant.
Continuity mistake: Doug goes to Deacon's to tell him about Kelly wanting to get back together. Deacon is putting on his shoes and in different shots, sometimes his shoe is almost on and then other shots it shows him holding it in his hand about to put it on again.
Continuity mistake: While Arthur tries to convince Spence about the card, when Spence bites into the fake cookie he's holding it in his left hand and holding the plate in his right hand, but in the next shot facing Arthur the items have switched hands. (00:16:30)
Continuity mistake: In this flashback episode, when Doug is shaving his mustache and talking to Deacon by his locker at IPS, Danny Heffernan's name can be seen on a locker. At this time, Danny was not working at IPS.
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)
Cheap Saks - S6-E15
Continuity mistake: Near the end of this episode, after Trish Flintoff leaves, Doug is telling Carrie and Holly that she's a nice person. Doug is looking at Carrie, then the shot changes and he is immediately looking down and reaching towards his back pocket. It also looks like he's trying not to laugh. (00:19:35)
Continuity mistake: In the scene where Doug's father is shutting off the alarm, he does not enter 2965. We know this is the proper code, because it is Doug's birthday, and it worked when he entered it. It looks like he maybe enters 1459.
Continuity mistake: Carrie says that she "didn't go" to college because Arthur felt that she would be abandoning him. He points out that her mother had just died. According to the episode "Class Struggle" (Season Two), Carrie actually went to college and then her mother died, causing her to drop out. In that episode, she wants to "go back" to college.
Tank Heaven - S6-E21
Continuity mistake: In the scene where Danny has just taken the "nucleus" nacho chip, after Carrie walks in, the chip in Danny's hand keeps changing between shots, then disappears altogether almost instantly and his arms are folded when he begins his next line. (00:02:30 - 00:03:25)
Continuity mistake: The second time we see Doug's disk, it is spinning. In one shot it is spinning in shadow, but in the second shot it is in the sunlight. (00:08:00)
Continuity mistake: During the first shuffleboard scene, the characters are brightly lit and cast by long dark shadows (indicating early morning or late afternoon), but when you see shots of the shuffle pucks flying into the bleachers, the bleachers' and extras' shadows are cast straight down (indicating noon hour).
Continuity mistake: When they are in the kitchen Carrie's purse switches from shoulder to shoulder when she tells Doug the good news.
Silent Mite - S7-E7
Continuity mistake: In the final scene where Arthur raises his ornament on the Christmas tree, the kitchen door is closed behind him. In the next shot looking out from the kitchen, the door is already open as Arthur walks forward and through it. (00:21:15)
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)
Deconstructing Carrie - S7-E15
Continuity mistake: In the kitchen when Arthur says he was a terrible father and gets up, Holly looks over at him with her hand on the edge of the table. She says, "Oh no", but then she's smiling. When the shot changes angle, her arms are crossed. Then Holly says, "Better than my dad, who was too busy chasing the almighty bottle of glue", her hand is instantly on the box of photos again. (00:11:35 - 00:12:05)
Deconstructing Carrie - S7-E15
Continuity mistake: Doug is sitting on the couch making club music sounds and moving his hands when Carrie reaches out and touches his face to make him stop; then his left hand is instantly on the arm rest. (00:13:10)
Deconstructing Carrie - S7-E15
Continuity mistake: While Carrie was being harassed by the construction workers, Doug was watching by looking out the door to the right. In the next shot, you see Carrie through the window, coming in from the left.
Move Doubt - S8-E8
Continuity mistake: Near the end of the episode when Doug and Carrie are at Deacon and Kelly's apartment, you can see a picture on the wall in the hallway behind them. Then when Doug and Carrie leave, the wall is much further back and there's a window and plant instead of the picture on the wall. (00:19:40 - 00:20:45)
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.