First, the price. The last paper I reviewed took me about 10 hours. I charge $200/hour. Should I charge $2000 for my time? If I'm paid by the hour, who tells me when to stop? If I'm paid a flat fee, how much is that fee?
I have seen a reviewer write something like "I read the paper twice. It seems good. Publish it." Does that get the same as someone who spends 10 hours for a detailed critique?
Second, does payment constitute work-for-hire? Does the publisher and/or reviewer need to pay taxes? Might some reviewers have a contract which prevents them from taking on part-time work? What if the reviewer is overseas? Do tax agencies from two different countries need to be involved?
Third, most people expect to publish, and get their papers reviewed. If a single author has three reviewers, then that author should expect to do about three reviews. This is an imperfect system which rewards publishing rather than reviewers, but there are also some compensations to the reviewer.
Moreover, I recall one story - I don't know the validity of it, but it has a ring of truth - where a daycare got annoyed with parents who picked up the children late. They decided to fine parents should that happen. As a result, children were picked up late more often because the fine was interpreted as a fee for extra daycare, and no longer social chastisement.
I suspect that reviewers are in a similar boat. I'll feel different about it if I get paid a pittance than if I were to do it for free, so long as others do the same for me in the future.
Of the people I meet at a conference, how do I figure out who has been a reviewer for Nature, and how do I verify that claim?