That's because many of the plugins are not completely ready for 64-bit.........
The Mozilla and Firefox browsers along with the java plugin (and others) should be 32-bit. Remove the 64-bit versions of the browser(s) and the jre and install the 32-bit version of the browser(s), warning you will need a couple of 32-bit libs for this. Mplayer and the mplayerplug-in need to be the 32-bit versions also, since the extra codecs are only for 32-bit.
The 32-bit java link should be in the /usr/lib/mozilla/plugin location.