Getting the bottom of the carboy spotless is a difficult, because the water pressure from the jet dissipates quite a bit by the time it reaches the bottom of carboy.
Have you tried soaking the carboy in water with a little dish soap? It'll help loosen up the crusties. Then scrub a bit with the brush and blast it with the water jet, giving it a really good rinse. Works like a charm for me...
Edit (Feb 9, 2013): I have become a faithful user of PBW. Let it soak for a while (or overnight), rinse well, and voilą -- the carboy is crystal clear.
Last edited by MoreHops; 02-09-2013 at 01:14 PM.
Reason: My method changed, so I thought I'd update my post.