Someday, as strange as it feels to me right now, I might be asked to review an article for publication. A while ago my advisor and I were talking about this, and it hit me that I don't really know how to be a good reviewer, beyond the basics:
Respond timely to things,
Make your report clear and detailed,
Have actually read the paper,
Beyond this, though, I'm completely in the dark. So I'd like to ask:
What's some good advice for a first-time reviewer?
My field is math, but I'm really interested in general advice (although advice specific to math, or another field, would also be interesting and useful).
I'd like to make this question "community wiki" or analogous, but I can't seem to figure out how - if someone can do so, please do, and then I will delete this paragraph.