Are you sure that your Logitech mouse is Bluetooth?
Most Logitech wireless devices (including mice) are NOT bluetooth.
For example, Newegg.com shows nearly 50 Logitech wireless mice. Of those, only two are Bluetooth. Your Logitech mouse would have a USB dongle that it uses to connect to the iMac.
Do you have the Logitech Control Center installed? Try uninstalling that. Your mouse should still function, and you can eliminate that as the cause of to sensitive left-click.
Have you also installed another mouse driver, such as Steermouse?
Be sure to try the mouse settings (in your System Preferences) again. Set the double-click speed almost (but not all the way) to Slow, then find something to double-click (opening a random folder, for example). Try that same folder a couple of times to get a feel for how that works. Then, move the double-click speed to (almost) the fast end. Try the same double-click again. You should find (toward the fast end) that double-click is much LESS sensitive, as you must double-click very quickly. The Slow end will be very hard to NOT double-click, as almost any second click will be accepted as a double-click, even a couple of seconds after the first. Be sure that you try your second click with more delay to see how that works...
Do you see any difference now?
If you have used the Logitech Control Center, and you prefer to continue using that software, be sure that you have the Lion-compatible latest version:
http://www.logitech.com/en-us/584/3129
And, if nothing else helps, be sure to try your mouse on a different computer. You may find that the mouse button is bad.... and, replacing the mouse is the fix for that.