Although current search is quite powerful, its big limitation is that it is unusable for searching within page - it does not find matches within words. I do not expect any engine to support partial word matches, but for searching within current page it would be really beneficial if there was a way how to find any string (including punctuation).
So i'd propose new Find in page (slow, powerful) function, separate from Search function (fast, limited) - or make Find behave differently in "Page" context, than on other context.
Regexp as an option, would be greap, but for the common audience, that would be probably an overkill (and the major advantage there are the replacements, so search alone is not that useful).