FWIW, Firefox handles alert() much better than Chrome does. In Firefox, you can navigate away from the page, and switch tabs. Chrome won't let me open a new tab, and keeps the alert in front of other pages.
There are still a number of types of dialogs that are not tab-modal. See https://bugzilla.mozilla.org/show_bug.cgi?id=616843 and the bugs it depends on. alert() should be tab-modal content, though, and is for me.
