Carrie is the only main character who never appears nude (she is either dressed or covered by something). Sarah Jessica Parker had a strict "no nudity" clause in her contract.
After the first season, the producers hated having to refer to phone numbers by tv and movie standards (beginning with 555) that they purchased two real phone numbers to use throughout the rest of the series.
Concerning the entire Wall Street/Stock Market scenes; Sex And The City was the very first production to film in the New York Stock Exchange since the movie Wall Street. They filmed these scenes at the actual NYSE. Because it was after 9-11, every piece of camera equipment, prop, costume, etc. had to be sniffed by bomb-sniffing dogs. This was the very first non-official event that was let into the Stock Market after 9-11. Every extra that you can see on the Stock Market floor was an actual trader. Also, Sex And The City got to open the real Stock Market, on the day the show premiered.
When Trey and Charlotte are viewed through the Tiffany window, it isn't the actual window. Tiffany would not allow cameras to film inside their store, so the show built a fake Tiffany window. But Tiffany sent their dressers to dress the window, to make it appear authentic to the real thing.
Carrie is carrying a small bunch of violets in this Parisian montage. What is interesting is that in France, traditionally, violets are the flowers that the husband gives his wife when he has disappointed her, or they have had a fight. Symbolically, the violets that Carrie bought for herself represent that she is continually disappointed by Aleksandr.
During this scene, Carrie states to the other girls, "If you want to do your patriotic duty as New York women, you will come shopping with me right now and throw some much needed money Downtown". According to the commentary, this is possibly the only direct reference to New York City and 9-11 in the entire episode. Downtown NYC was very hurt by the World Trade Towers disaster, and the show thought that Carrie's character would be doing her part, which includes shopping.
During the scenes in the department store, they were filming at the real Barneys. Also, the blindfold that Charlotte is wearing is from Burberry. The show asked if they had Burberry blindfolds, and they didn't make them at that time. But they then tailor-made a Burberry blindfold, just for Charlotte to use in these scenes.