Can the Dictionary Be Wrong?

I had a student look up a word in the dictionary the other day and complain that the dictionary was wrong. Is this possible? Aside from a typographical error or an omission, can a dictionary entry be incorrect? Is the dictionary scientific documentation of how words are used by the linguistic community or is it a prescriptive rulebook that dictates how we ought to use words? If I look up a word and the dictionary says it means one thing and I think it means another, who wins? If I lose that battle, how many people do I have to gather on my side before we can start a revolution and overthrow our lexicographic overlords?