For what it's worth, I've just stumbled over some strange behavior. I have Netscape 4.7 set as my default browser. In this session I had NN4.7 and Opera 5 both open, and I was clicking on some PDF links in a newsletter in my Netscape Messenger email client.
My first click on a PDF link opened in an Acrobat Reader window within the Netscape browser, as expected. But my second click on a PDF link opened its page within the Opera browser!
I spent some crazy minutes looking for the page, because it didn't get focus and remained behind the stack. This is the most blatant tangle I've seen with more than one browser open.
More commonly, one or more browser just starts acting buggy at some point in the session. I suspect (but can't prove) that this comes from having several different browsers open at once. For instance, all of a sudden links won't work in one window, or I can't minimize one or more windows.
This is first cross-browser conflict behavior I've actually been able to duplicate -- recreating the same conditions and getting the same result. Of course, who except crazy, obsessive web designers and marketers would open different browsers at the same time, anyway?