I haven't found a definitive answer to this question since there seems to be so many related questions.
** Does openjdk / icedtea have the same vulnerability?
** Is it specific to only Java7 or is Java6 also affected?
I do not have the answer but if you go to the following site it will check what version Oracle ( and presumably any evil-doer ) thinks you are running:http://www.java.com/en/download/testjava.jsp
On Mint14 it will come back with:
Java SE 7 Update 09
On Mint13 it will come back with:
Java SE 6 Update 24
You can always disable the plugin in Firefox: Tools > Addons > Plugins > IcedTea > Disable. You can go back to the link above and retest it to see if it gives you a "This Plugin is Disabled" error.