I agree with David: I think that my job as a referee consists mainly in checking that the proofs are correct.

However, checking that the proof is correct can in practice not be done by line-by-line checking. Referees are not computers, nor are the writers of the articles. Rather I have a kind of critical, "falsificationist" approach. I try to see what are the principal steps of the proof. If the article is well-written, this work has been done by the authors. Each of those stepsis an assertion, and I try to disporve it. Is it in contradiction with something I know? Can I find a counter-example? If I can't I begin to believe a little in this one step, so I try to prove it myself. If it's too hard, I read the proof of the argument (if there is one!) and apply th same method th understand and check it.