Continuity mistake: When Arthur is telling Carrie he has got a job, Carrie is putting out paper plates. She puts all three out and then the camera changes angle. When it does, one of the plates has moved across the table and Carrie is seen placing it in position again.
Continuity mistake: In the scene where Arthur is on the phone with PBS to complain about getting a "Civil War Series" box set, the actual set of tapes changes drastically. When it's on the table and when Carrie brings it over to the counter its a pretty large, has an American flag motif, and says "Civil War" across the top. When it cuts back to it sitting on the counter its a much smaller box with a plain design and says "The Great War" along the bottom. It's obviously a different set, not just the camera angle.
Continuity mistake: When Carrie confronts Arthur about looking in her bag, her bra strap is slightly hidden by her top. Camera cuts to a front view of Carrie then back to behind her. Now her bra strap has moved and is totally visible. Carrie never touched it during this time as we see her hands.