One of the flaws, it seems, could be used to potentially log keystrokes. However, the flaw was isolated to the 7 series player, which has long since been replaced by versions 8 and 9. Regardless, those versions as well have independent flaws, making an update a good idea. If you are using the player, it's a good idea to update.
This is another cross-platform flaw, too, affecting Windows, Mac, Linux and Solaris. Adobe is recommending anyone using the players update immediately.