Will writing MSC instead of MSc in an application count against me?
While it is possible for an applicant to be harmed by sufficiently bad grammar in a personal statement, I cannot imagine something on the scale that you describe -- writing MSC instead of MSc -- having any impact whatsoever on the evaluation of your application. Bad grammar can count against you because it indicates that you are not be a poor writer and/or you didn't take time and care with your application. Switching between MSc and MSC signals neither of these things, so you should be fine. There are so many ways to sell or sink an application that something on this scale is miniscule noise compared to the other signals that an application provides. 

Note, by the way, that there is some variation allowed in this abbreviation, though I don't think MSC is among the accepted forms.