In my personal opinion, asking a lot of questions revolving around a single topic is definitely better than slapping your topic down on the table and taping a question mark to the end of it. Rather than asking one question that's too broad, series questions seek to split up their general lack of knowledge into manageable chunks that can more easily be digested by answerers. I think this is a good thing.
One problem that I've often noticed, though, is that the answer to most of these questions depends on the answers to the other ones. In your example, you can't really say how the police would be trained to fight stun-gun-using bad guys until you know what laws are in place for the use of stun guns. Likewise, it might be difficult to say what laws would be put in place for stun guns without knowing how the police could respond to them. In situations such as this, I find myself in an answerer deadlock, and can't focus on one question without focusing on the others. For this reason, not only have we gone back to the initial too broad problem, but now no one can even provide a good answer without splitting it into separate pieces or copying it into the other questions.
I don't even think the temporal distance between questions is of any use here, because asking one question while leaving the other for the next day might mean that that second question ends up getting answered in order to answer the first. Thus, either you see both questions and can't answer either, or you only see the first and end up answering all of them by accident.
For this reason, I'd say there are still cases where asking a series of questions is just fine, but that you can't always split up a broad question and expect it to be improved. That hunting question looks like it could stand on its own to me, but the law and police questions are just too closely coupled to be split up.