If you had trouble consistently hitting targets, you would probably fit right in with Patriot missiles.
http://en.wikipedia.org/wiki/MIM-104_Patriot#Success_rate_vs...
http://en.wikipedia.org/wiki/MIM-104_Patriot#Success_rate_vs...
Think about the margins of error involved - how precisely do you have to know the Patriot rocket's position, vector and speed to intercept something falling from space? How do you take into account the fragmentation issues of a device like a MIRV? How do you account for any differences in the target projectile's path?
It's just an astounding problem to me. I very much dig the thought that I'm the same species as those that figured it out.