Deconstructing Carrie - S7-E15
Visible crew/equipment: When Carrie comes into the house after being hit on by the construction guys, a shadow (boom mic) passes over the TV. (00:12:45)
Revealing mistake: When Doug and Carrie are waiting in line at the DMV, a man (casting extra) can be seen just outside the doorway waiting to enter the scene. When the shot changes and Doug and Carrie approach the counter, the man casually enters the set. (00:03:30 - 00:04:00)
Visible crew/equipment: When Doug and Arthur are eating in the buffet restaurant, stage lights are seen reflecting in the cup. Also, each time the camera goes from angle to angle, the cup has moved from one side of the table to the other, sometimes have a saucer, sometimes not. (00:06:35 - 00:08:20)
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)
Visible crew/equipment: When Carrie is sitting on their bed talking to Doug about falling in love with her pretend (model home) family, you can see the shadow of a boom mic move on the closet behind her. (00:13:25)
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)
Visible crew/equipment: When Carrie and Arthur pull into the driveway, the camera is reflected in the car. (00:18:15)
Visible crew/equipment: When Arthur is hinting it's his birthday soon, there is one shot where you can see the cupboards above the hatch into the kitchen. In this shot you can see a boom mic follow Arthur across the room. (00:02:30)
Visible crew/equipment: When Carrie goes into the kitchen and Doug is seen through the window getting burnt, the boom's shadow can be seen moving along the wall by the window. (00:14:45)
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)
Soft Touch - S2-E22
Visible crew/equipment: When Doug gets into bed after arguing with his cousin, a camera shadow can be seen moving over the bed. (00:17:45)

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.
Revealing mistake: Just as Arthur goes to look in Carrie bag, there is a wide shot and a cabinet can be seen by the door. In the glass of this cabinet's door, you can see a stage light reflected. (00:11:45)
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)
Answer: Sara hasn't been mentioned in later episodes, and it suggested in later episodes that she never existed, and that Carrie is an only child. Kevin James stated that the producers couldn't think of an good plots to use with Sara, so they left her out.