Kim Cattrall turned down the role of Samantha Jones twice before being convinced by Darren Star's boyfriend to give it a try and shoot the pilot episode.
In the earlier series, the exterior the Carrie's apartment was another apartment block (in one episode we see a couple having sex through this windows). In later series, the exterior changes to the street outside and the other apartment seems to have moved.
In the opening credits, a close-up of the bus that splashed Carrie shows that it was full of people. But as the bus rounds the corner, it is totally empty.