Okay, well ' is the keyboard shortcut for "find link as you type" and / is the keyboard shortcut for "find text as you type". Neither is supposed to be active when your cursor is within a text box. There was an old bug with an earlier version of Firefox, which has since been fixed. The partial solution then was as follows:
1. In a blank Firefox tab, type about:config in the address bar
2. In the filter box, type dom.disable_window_flip.
3. Double-click dom.disable_window_flip in the list to change it to TRUE.
This can interfere with certain javascript. Try it, and if it doesn't fix your problem, repeat the steps to set it back again to FALSE.
I haven't found a specific fix for the problem with current versions of Firefox - you may want to post this on Bugzilla, if you can reproduce the bug. In the meantime, if you happen to find that you're in the FIND box unexpectedly, pressing ESC will get you out of there.