One question bugged me for a while now: what's a "top level comment" and is it some kind of a privilege to make one? Is it the article itself, or a comment that's not a reply to a comment? (Since no one got mad at me yet, I either haven't made one, or nobody noticed).

The first; a top level post is the article itself. Unless it has been changed recently, making a top level post in the main section takes 20 karma, while making a top level post in the discussion section is something anyone can do.

Also: what's the etiquette on editing after someone's pointed out a flaw in my post? It reduces on verbal clutter if I just went back and edited, but might put the rest of the comments out of context. Especially if it's a major reasoning flaw that you can't just put in under "EDIT: "

Like TheOtherDave, I would prefer posts not be edited such that previous information was lost. You can write something like "EDIT: <user> pointed out below that my argument is flawed because. of <x>" or "ETA: My argument is flawed because of <x>, as <user> made me aware of" at the end or beginning of your comment, or right before or after the section that is most adequate (use italics if you fear creating confusion between the edit and the rest of the post).

And also: if I accepted someone's correction and edited, should I add to verbal clutter by posting "thanks," or do my actions (edit + upvote) give enough evidence to the fact that I'm thankful?

So long as you are editing your post in response to someone else, adding a small note of gratitude there seems most appropriate.