I use ubuntu 11.10 in a tablet and I had the same problem with the scrollbar. I don't have a perfect solution, because it depends on the theme (If you're not sure what theme are you usnig install ubuntu tweak to serch it; mine is Ambiance) and the programs that you're using, but I follow those steps and it's OK for me now:
1- Remove overlay-scrollbars (for unity)
2- Edit /usr/share/themes/Ambiance/gtk-2.0/gtkrc and increase those values
GtkScrollbar::slider-width
GtkScrollbar::min-slider-length
3- Edit /usr/share/themes/Ambiance/gtk-3.0/gtk-widgets and increase
GtkScrollbar-min-slider-length
GtkRange-slider-width (there are several items, look for the one inside .scrollbar)
I've increase length to 51 and width to 23 and I'm happy with those values in my tablet (11.6" - 1366x768 pixels). You need to modify both files because gtk2.0 controls for example firefox and thunderbird, and gtk-3.0 controls for example nautilus and gedit. There are lots of tweaks that you can make in both files, I've added
GtkScrollbar::has-backward-stepper = 0
GtkScrollbar::has-forward-stepper = 0
to /usr/share/themes/Ambiance/gtk-2.0/gtkrc to remove the ugly arrows in firefox and thunderbird.
You can see some pictures, all of them with my minimum scrollbar width and length:


Good luck!