This seems to be an issue with the Firefox's default theme, to it should be fixable by a tweak to that theme. Probably a simple change in chrome's CSS as Nick Welch suggested.
When I install the Classic Compact theme (https://addons.mozilla.org/en-US/firefox/addon/3699) and its configurator (https://addons.mozilla.org/en-US/firefox/addon/6969), then configure Classic Compact to "Webpage window border: Disabled", then the scrollbar works fine at the edge of the screen.
This is on the current official Ubuntu Firefox 3 package for Hardy (firefox 3.0+nobinonly-0ubuntu0.8.04.1).
The Default theme shipped with this package still exhibits the problem.