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.
During the opening credits. the city bus that splashes Carrie with water and has her ad on the bus. There's passengers on the bus. But in the next shot where Carrie turns and the credits end. The passengers disappear.
Recurring throughout most titles: extras can often be seen staring at the camera, because they are non-paid New Yorkers and the show was filmed in the middle of busy streets. They aren't so much extras (which means "paid background people") but real-life people, going about their lives. If they're not paid, they cannot be asked to not stare at the camera. Accordingly, they are often blurred in the perspective background, but some can even be seen taking photos of the actresses during filming.
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 fourth season, it's shown that there is an apartment next door to Carrie, and Aidan purchases it so he can merge the two units. He is shown punching through the wall where Carrie's headboard is usually placed, which would put the apartment to her left, though the exterior of her building is too narrow to have two units placed side-by-side like this-the exterior only has three windows, the same as Carrie's apartment.