I have seen a couple of threads about users on Windows having to reboot after installing the Flash Player 6 in order for the player to be updated. This is not new to Flash 6, and is actually an issue with all ActiveX controls (and not specific to the Flash player).
To find our more information, we have a technote on the issue (notice the date on the technote).
This issue is also covered in the:
Macromedia Flash Player Support FAQ