I regard it as *part* of my job as a referee. But the amount of time I spend checking proofs really depends on whether the point of the paper is to prove something I already believed but didn't know how to prove (in which case I spend a lot of time) or to tell me something new, in which case I might spend very little time on the proofs and rather focus on deciding how interesting the new facts are.

I agree with the oft-expressed sentiment that it is primarily the responsibility of the author to check for correctness. Editors may well find your assessment of the value of the theorems contained in the paper more useful than your assurances that the proofs are correct.

Someone who is interested enough in the results of a paper to use them is going to be the most likely source of corrections for the proofs. I've found more errors in papers whose results I needed to apply than in papers I've officially refereed.

Edit: I think it's worth responding to David Feldman's answer. I agree with his aim: ensure that mathematics literature is not full of errors. But I think that the refereeing process is not the most efficient means for weeding out inaccuracies. Better for that to happen organically as the consumers of new ideas put them to the test. The arxiv helps quite a bit, by ensuring that ideas are disseminated quickly to those that are likely to appreciate them. Why centralize this process? Furthermore, even with the most conscientious refereeing, mistakes will slip through if the only two people who have read the paper carefully are the author and a reviewer (and if those really are the only two people who have read the paper carefully, then it's probably not a big deal that an error made it through, anyway).

Roy Smith's comment below is a good one: if you don't have time to check the proofs carefully, tell the editor that. S(he) can then make an informed decision about publication. Often I receive a request to referee a paper that I am sure I will find useful at some point in the future, but I don't have time to check carefully all the proofs (real life and other work can get in the way). I could tell the editor to find another referee, or I could do the best I can in the time I have. Sometimes I really think it's better for the mathematical community to choose the latter, since finding someone to referee a paper can sometimes be a real timesink.

Perhaps the disagreement here is a cultural one: some people think of mathematics as an experimental science, some think of it as primarily about finding the right answers, and some think of it as primarily about finding proofs. In the last case it's natural to put a premium on proof checking.

oughtthe job of refereeing be (in an ideal world)?", there's "What is the actual job of a referee?" (which is unanswerable), and "What is the job of a refereefor a particular journal?" which has the answer: "If you're not sure, ask the editor who referred it to you.". $\endgroup$ – Loop Space Oct 1 '10 at 11:05you should make reasonably sure that the work you refer to is free from error. At the very least, check Mathscinet to see if the journal has posted a retraction. Sadly, I speak from multiple experiences. $\endgroup$ – anon Dec 12 '10 at 23:54