The Constitution was crafted to be a living document. It was left deliberately vague in many cases due to the fact that the Framers had the foresight to realize that they couldn't possibly know what specific issues would arise in the future--and which issues that at the time seemed vital would later fade to obscurity (the 3rd Amendment comes to mind here).
But the changes to the Constitution were not meant to be done via the Courts; they should be done via amendments.
Marbury v. Madison?
What do you mean?
Sorry, made a mistake. Disregard that statement.
Anyway, isn't it the courts' job to interpret the law and, by extension, the Constitution?
Yes, it's their job to interpret the law and the Constitution (altough I'd argue not by extension - I'd argue those two are different in their origin, although same in ultimate outcome... a small difference).
Were the civil rights cases (Brown v Board of Education and stuff) not interpretations of the law and Constitution?
Yes. They were. And equal protection under the law is something that should be enforced in schools, because that's a public institution.
But private institutions can defy the Constitution all they want, right?
It depends what the issue is. Take the First Amendment, for example: if a private company wants to restrict speech, that's their right. What authority, under the Constitution does Congress have to say a small diner can't have separate seating for whites and blacks? In my opinion, they don't. Does that mean I think diners should be able to segregate seating? Absolutely not.
The SCOTUS unanimously disagreed with you. Remember this as you enter 1L.
http://en.wikipedia.org/wiki/Heart_of_Atlanta_Motel_v._United_States