When Mr. Big offers Carrie a ride, his car windows aren't tinted. When she gets out and asks him a question, they are tinted.
@4min, the close-up of Carrie's column in The New York Star shows that the text simply repeats in order to fill the space on the news page.
When Carrie first bumps into Mr Big there are two women next to a building clearly watching the actors and camera crew.
Carrie refers to Elizabeth as an "English" journalist, but as soon as the character speaks, she sounds Australian (and the actress playing her is indeed Australian).