Then I installed the AJAX login plugin for my buddypress enabled site.
In my right column, there was an ad manager ad above the ajax login fields, and if any of my users using Chrome or Opera clicked in the login fields, they'd be instantly directed to the URL of the ad above that widget.
I initially thought this was a problem with the Ajax login plugin, and contacted them. You can see that thread here: http://netweblogic.com/forums/topic/plugin-not-working-with-google-chrome-or-safari
Eventually, I created a fresh installation of WordPress with Buddypress, and installed only two plugins: the ajax login and advertising manager. Even with a clean install on the default template, Ad Manager behaves the same way with Ajax login (and presumably other java related ads).
You can temporarily see this problem in action, here: http://www.goreorchidconservatory.com/affblog/
Note that the AJAX login is the one BELOW the ad on the right column.