Sorry to beg your pardon :-) but it is no question of caching. I was formally (two weeks ago) using a very old version of Mantis that had the same issue.
You mustn't rely on the browser caching. That is not the way it must work. Why can't you just display the same form again, filled with the datas and with an error message on each problematic field?
This is the way any form on the web works.

It has been fixed that browsers will keep your form data for you now, so that in itself is fixed, and yes, it was broken in older versions too, so hopefully it will stay fixed this time.

Otherwise, you must remember that Mantis is a very old and mature project, predating "web 2.0" garbage by a good six years. It doesn't use any of the new fancy technology that makes form handling and validation trivial, and it doesn't require javascript-capable browsers. We don't have the contributors to sustain the effort needed to basically rewrite the entire application from scratch to use modern techniques either, so it's not going to be rewritten just because it has a few rough corners.

And in all seriousness, if you're that caught up over the method used to validate what little required form data we have, perhaps you should either find a project that better suits your tastes, or you should learn to fill in those three fields before submitting...