Latest version of "com_comprofiler" shows that's using version 1.5.2 of jQuery, while my template is using v1.6.4. This causes mainmenu on my site (Joomla) to disappear. Is it possible to have com_comprofiler use a different version of jQuery than 1.5.2?

I would recommend setting you're template jquery in noconflict mode.
I actually have to use a few different jquery versions on one of my sites along with mootools so I set the dollar sign variable differently for each jquery version using something like var $jq = jQuery.noConflict(); then you just go through your scripts using that version of jquery to use the $jq instead of $.