Let's go through these a little more carefully:
- Content that is in violation of "be nice" policy (that can't be edited to remove violation)
- Content that is in violation of other policies (spam, mostly)
I think these are reasonably uncontroversial. Flag 'em with "rude and abusive" or "spam" as applicable.
Side note: The Smoke Detector folks would really like it if we did not spend deletion votes on spam, but that seems to be more controversial based on the upvoted answers. I would encourage 10/20k'ers to use their best judgment here. If you can't vote to delete, then obviously you should use spam flags (and not e.g. "very low quality" or NAA).
We seem to get into fairly regular arguments over the definition of NAA. OTOH from my experience, that's a problem on just about every SE site.
It is pretty uncontroversial, across the entire network, that "thanks" and "me too" answers should be flagged NAA. As the link above shows, our SO friends have (or at least used to have) the policy of keeping just about everything else. However, our policy is different: An answer can be flagged if it is clearly and obviously irrelevant to the question (e.g. "Why didn't Voldemort do a better job of hiding his Horcruxes?" - "Because Sauron doesn't find Frodo when he puts the ring on.") or if it goes off on an irrelevant tangent without addressing the body of the question.
Answers that objectively add zero value (not simply low quality, but really can't be fixed).
You can't just put the word "objectively" in a sentence and magically make a subjective thing objective. Sure, there are a small number of really obvious cases, but most of those...
Note that this doesn't apply to questions - first, a question's objective value can be its answer; second, it's far easier for subject matter expert to judge if an answer adds value than a question, from my experience.
...also apply to questions (e.g. a question or answer consisting of pure gibberish can and should be flagged for something, and it's unhelpful to waste too much time hand-wringing about which flag option to choose).
The main exception that I can think of right now is an answer which is largely or entirely duplicative of another answer, and yes, those should absolutely be flagged and deleted. In contrast, we don't delete dupe questions because they are at least marginally useful as signposts (which dupe answers are not because they're already on the same page anyway).
There are other exceptions which I have missed. I am not going to exhaustively run them down because the users of this site have common sense and the ability to think for themselves. The important point is to think really hard before calling some particular case "objective." If you're not sure about something, take it to meta and we can talk about it.
Content that is unambiguously trolling and thus has no redeeming value. As in, no reasonable user based on evidence would disagree that it's trolling.
Note that this does not include "some people dislike some types of questions while others don't think it's trolling" situation, which many of the incidents being discussed here fits.
Formatting in DVK's original answer.
This is also uncontroversial, but don't ignore the bolded parts. Don't call someone a troll just because you personally think they are trolling. Don't call someone a troll just because "it's obvious." Don't call someone a troll just because "some users on this site are really obstinate in recognizing trolling." None of those are OK.
Finally, a case that you missed: Lots of questions get automatically deleted and we can't turn that off. However, relatively little user discretion is involved here (aside from downvotes accelerating the process), so there's not much for us to do with these in any event.
There is a discussion in the comments of the question about whether adult content should be eligible for deletion as well, but consensus points to "no," and I see no reason to rehash that argument here.