FearNot. This Wiki suffers more from lack of editing than from too much. People here are not as uptight as you might think (at least, the people who matter aren't).
Don't refactor live threads. When people are still going at it hot and heavy, let 'em be. When they all get too disgusted with themselves to contribute any more, still let 'em be. Give it a few weeks for the dust to settle. Then try to fix it. (Hint: if you got there from RecentChanges, the thread is probably live.) See RefactorFasterDeleteMore for counterarguments and exceptions to this rule.
Fix your own mess first. Don't go round refactoring and chopping willy nilly. FixYourWiki before you even try to fix anyone else's stuff.
Fix grammar, spelling, and factual inaccuracies. Spelling and grammar improvements are always welcome. Also fix any factual inaccuracies, as long as your change doesn't affect the meaning of the surrounding text. There is no need to add a comment to point out the original author's inadequacies or your own expertise: just fix the things that need fixing. Be sure to check the "I'm just doing minor edits" box when saving.
StopTidyingWiki. Sure, it's all crap. Yes, you're doing everyone a favour cleaning it up. But sometimes, someone, somewhere, is going to want that crap back again. Save it. If anyone wants it back, put it back. Don't argue about it - that'll only make it worse. Just put it back. The best work is done in small steps. (See also VersionControlAppliedToWiki.)
SummarizeAndSeparate?. Most threads include opposing viewpoints. Sometimes you can refactor those viewpoints into little paragraphs on different pages and add links to the opposing pages. Where there are repetitions of existing material elsewhere, this allows you to collapse them.
LetItBe. If you can't see a neat way to clean up a mess, let it be. Someone else will figure it out. Don't hack something out just because it's ugly - let someone else have the chance to figure out how to set it to rights.