Hmm.. I'm not sure about this. Yes, you won't get dinged based on this mistake only, and your's definitely won't be the only such mistake. However, it doesn't do you any favours. I keep coming across numerous blog posts where the Adcoms exasperate that they keep receiving applications with mistakes as "BAD" as having the wrong school in the essays.
I agree with GMATLA that you shouldn't contact the school about this. They're bound to spot it, and your drawing attention to it is not going to help one bit.
All said, if you have a stellar app, this shouldn't affect your chances.
GMATLA
Another classic case of "DON'T READ YOUR ESSAYS AFTER YOU SUBMIT THEM"! There is nothing you can do now, so finding a mistake will only drive you crazy
I agree, unless it was a case of using the essays as a reference for another school's app, and then stumbling upon the mistake. I prefer starting each school's essays from scratch any only referring to previous essays if I've been struggling to get anywhere for weeks on end. This may not be possible if you decide to apply to a couple of schools with only a week left (as I once did)