Browsers are the wrong place to report HTML validation errors
A popular idea for dealing with 'malformed' HTML is to have the browsers warn users about it (the most recent example I've run across is in comments here), on the theory that this will cause authors to make their HTML validate. Unfortunately, doing this is about as useful as showing error pukes to website visitors, and for the same reason: it is reporting the problem to the wrong person.
Almost everyone visiting your site is a visitor, not the site's author. It follows that almost every time this hypothetical 'page is malformed' error would go off it would go off to a visitor, who can't do anything about the problem, instead of to the site's author (who can).
The usual retort is that the site's author can visit the page as the final step in publishing and see the warning and do something about it. This is a marvelous theory, but (I argue) incorrect in fact, in part because it assumes that site authors actually bother to check their work, and in part because it assumes that site authors are going to notice a little status notice any more than they notice any of the other little broken things that they let slip by now.
(And if site authors do care about validated HTML they are probably already using one of the validation tools to check their pages, and this feature would not be a particularly big bonus to them.)
This is also a terrible feature from a pragmatic user interface point of view: on today's Internet, it would be the boy who screams wolf all the time, because a rather large number of the pages out there do not pass validation. Such a warning notice would be on a lot; if it is intrusive it gets in your face almost all the time (about something you can't do anything about), and if it's not intrusive it's pretty much a noisy waste of space. This is not a winning user interface element.
(But if you really want it, you can get Firefox extensions that do this.)