If you have any problems and can't get a fix, don't leave it too long as the next version of the game, KOTOR 2 Plus, is slated to be released in February 2005. There's also a Player Upgrade program - if you're still having problems, it may be worth taking a look at that option. If you're still having problems it's possible that a custom modification of the file will work.
The KOTOR 2 installer is much more trouble than it needs to be. It installs fine, but after the initial install you'll need to do a reinstall because the installer does not install all of the the 32bit and 64bit libraries for the game - after installing it you'll need to go to Tools/Xbox-360 Settings/Updates/Client Updates/Install, follow through the install, then run the game. This means you will need to uninstall/reinstall the game a total of four times to get the game running correctly. To get around this, you'll need to manually install the libraries on your own, but there are a few things to watch out for.
KOTOR 2 will install a new folder in your My Documents folder (or on a removable disk, a new folder will be created on the disk). If you want to check if the installation was successful, open 827ec27edc