A Day in the Life of a Puzzling Moderator!
Moderation of Puzzling is actually pretty straightforward, and not as soul-sucking as it might seem. I only give a little blood to the blood gods, and that's only on Tuesdays and every day of the waxing moon.
The number of moderator-handled flags varies from day to day, but this month, the team handled a total of 122 flags, at around 4 a day. This quarter, 412 flags, at about 3.4 a day. This is a pretty bad sample, though, because most flags are automatic flags raised by Community, and are largely pretty easy to handle. (Another significant fraction are notes I've left to the team to follow up with answers that have no explanation.)
I can't really comment on how much time a day is required, since I typically spend a lot more time watching the site than would be, strictly speaking, necessary. Mostly because I like moderating, honestly. I've grown into a habit of checking the site pretty regularly, when reasonable. Checking flags, meta, and chat is usually sufficient.
The average flag gets handled in about four hours. That includes a lot of flags mods don't see, though - stuff that goes to the VLQ and close vote review queues first.
At a guess, most flags take less than a minute of attention to handle, but some will eat up a fair bit more time. However, when I started out as a moderator, things tended to take a bit longer. There's definitely a learning curve.
The real time-consumer is plagiarism. (And, again, a huge thank-you to all those who flag plagiarism. I can't emphasize this enough. These flags are invaluable.) This probably comes up once a month or two, but is the sort of thing we don't want to delay on.
When someone flags plagiarism, and it turns up positive, it requires a thorough searching of someone's entire question history. Sometimes, it's easy, when it's caught early. Sometimes, we end up deleting 20 or 30 questions (though a handful of proactive flaggers have, recently, headed this off early). We need to discover a verbatim source for each puzzle that we can reasonably verify was posted before the puzzle was posted here - or, alternately, perform enough searches to convince ourselves the puzzle wasn't plagiarized.
On the other hand, this is something I do with gusto. Plagiarism is extremely unethical, and any time I spend fighting it is time I consider well spent.
As a final note, vote fraud is pretty rare, all things told. I can count the significant cases of vote fraud on one hand, and most of those warranted community manager assistance to handle correctly anyway.
If there's something I didn't touch on, or needs clarification, let one of us know, either here in comments, or in the election chat!