Hi Rob,
I have investigated the page (was doing some Safari debugging today anyway, not a specialist by the way).
I do know Safari does not handle Javascipt / HTML errors very well, it's very strict.
I made some screen captures with element info, if you send me an email, I'll send them to you.
It seems to me there is no relationship with the serach input, so it might be one of the other hidden inputs or one generated with javascript.
I also tried to save the page and open the saved HTML in Safari, for debugging, but then none of the input boxes show up.
Even if I set all of them to visible and the background-color: red, the extra box is not there.
I noticed one more thing:
On the page there are two </body> tags, one before the injected navmenu script and one at the end of the page...
Could that be the problem? (I guess you accidently left one in your skin)