A common issue I've seen raised in comments is that a comment attempts to answer the question, and either ruins the puzzle or is annoyingly misleading. They may also simply be noisy or unhelpful.
This seems similar to the issue of spoiler-tagging answers, which is common practice so as not to unintentionally ruin the puzzle for someone else.
Should moderators delete comments that attempt to answer the question?
What about comments that make progress toward an answer without fully providing one?
In general I'm strongly against moderators deleting comments unless they're actually offensive or spam. And there's a big grey area here: attempted-solution comments vary hugely, from wild guesses through partial answers to full solutions. That said, here are a couple of possible solutions to the problem you raise.
Is it possible for mods to convert comments to answers in the same way as you can convert answers to comments?
If not, you could delete the comment and create a community-wiki answer crediting the user who posted the comment, to be deleted if they repost it as an answer.
Of course neither of these should be done (IMO) unless you've already asked the user who posted the comment to repost it as an answer and waited a while for them to do so.
I just thought of another point, important enough to deserve an answer to itself.
Solving puzzles is often a joint effort. Often one person comes up with an idea which is helpful to answer the question but isn't an answer on its own, and then somebody else follows up on that idea and expands it into more of an answer. That first person would often be better off posting their idea in a comment than in an answer.
Now I personally am a great one for posting partial answers - my record shows that I've posted a huge number of answers which weren't accepted - but others don't have the same style. And sometimes I come up with an idea which even I don't think is worth posting as an answer.
An example (which is actually what made me think of writing this answer). I think I may be onto something in that comment, but I'm not sure. If I posted an answer, it would be low-quality and deservedly attract downvotes. But the comment I left might inspire someone else to come up with a better answer. This is good. The spirit of cooperation in solving puzzles is one of the best things about this Stack Exchange. Let's not attack it!
The change proposed by @Emrakul sounds like it would mean comments like that one would be deleted before anyone had a chance to see them - although he said that actually he didn't think it warranted deletion.
I think answers in comments should be deleted.
Comments are intended to be used for requesting clarification from the author, not for answering the question. The comment box actually says so itself:
Use comments to ask for clarification or add more information.
Comments are supposed to be temporary post-it notes, not permanent answers.
Answers in comments don't normally contain enough information to be high quality answers. Almost all answers in comments lack an explanation - and even if they do contain one, it's typically not good enough to be worth answering with. However, if a comment spectacularly answers the question, it can be converted via community wiki.
Because this happens so often, following up on everything may be impractical. History with answers has shown that most of the time, people don't come back to edit their answer to include an explanation upon request (~85%). In the interim, while we wait, the additional comments will create more noise, and hide other constructive comments.
Consequently, I suggest we just delete comments that answer the question, and maybe in a rare, exceptional case, manually convert to answer or ask someone to answer.
