In episode one of season one it shows Carrie typing on her computer in her apartment. If you notice, she is on an older desktop computer, not her usual laptop, and her apartment is completely diferent from every other eposode. Very trivial, but something to notice...
The explanation for this slipup is that episode one was a pilot episode, and therefore was only going to be commissioned for a full series if it did well in the ratings war. HBO etc will have designed the apartment and computer 'look' for the full series after the pilot aired, so it will naturally look different from the rest of season one as more funding was invested in its development.
There are other examples of this type of slipup in other television series, so look carefully at whether the very first episode was in fact a pilot. It explains a lot of differences.