I know that gaining points in one primary direction will allow you to unlock special items, but I was wondering how it affected your standing with your chosen faction. If I'm playing as a Jedi of the Republic, and go down the dark side path, do I become a Sith and/or have the option of joining the Empire? Do other Jedi or "good guys" respond less favorably towards me?
You cannot change factions in TOR — what you pick is what you get.
That said, there are small differences depending on whether you are Light Side / Dark Side, such as verbal cosmetic changes in conversation. And your choices may affect companion affection.
Flashpoints are repeatable and have up to +/- 250 points' worth of dark/light decisions among them, and Diplomacy crew missions can yield DSP/LSP as well, so you can always completely reverse your stance (although that could potentially take a /lot/ of work...).