On a custom plone 2.5 skin we found that the livesearch results were getting overlapped by certain elements of the content including action menus and elements within a composite page, in IE6. After much trial and error this turned out to be because I had used absolute positioning on the search form, which obviously confused something somewhere along the line. I also had to remove position:relative from a couple of containing elements to get it to work. As this was a custom skin already fairly heavily modified (both css and template changes), I haven’t narrowed down exactly what was happening yet, or if there is a better way to address it, but I ended up moving the form and using floats and margins to get it in position.
The plone livesearch template and CSS code seems a little over-complex to me, and I don’t really like the use of an HTML fieldset to render the results, as this is always the first thing I break during a customisation so I may create my own version in due course (in private of course, before I go around claiming I have a better version than the one that ships with plone!).