This rocks! According to this article, carbon nanotubes may have the capability to spontaneously repair themselves.
One of the major concerns about a carbon-nanotube space-elevator ribbon is, of course, the damage it will receive when deployed. Meteors, atomic oxygen, radiation, salt water (at spaceport level), etc., all have the capability to wreak havoc with such a structure.
This article seems to indicate that there are some inherent properties of the material itself which would offset/mitigate these problems.