Many people would not agree with me, but here's a different viewpoint.
To me, criticism of videos is about 90% useless. I, for one, have never improved from the critique people have given me, but that doesn't mean I don't want it. I like it when people look into my video in depth, and I don't think it's a waste of time for the other person either.
Personally, I know every little thing that's wrong with my videos. I can name every instance in which there's something wrong, and there's typically 1 at least every 5 seconds. To me, something that's wrong probably isn't wrong to a lot of people, and that's why I typically release flawed videos, even though that sounds weird. People don't typically seem to care about those little things, or even the big ones, or even seem to notice them. I'm not saying everybody else is stupid and I know everything. I'm just saying, as an editor, I know my videos in and out. When someone points out a spot that is wrong, 99.99% of the time, it's something I already know, and that's why I'm never disconcerted or surprised when people point out those things. So I don't have a problem releasing something that's flawed in my eyes, or flawed in others' eyes, because I always feel comfortable knowing that it's flawed to
me, and nothing any body else says can make it any more flawed.

I'm also just lazy and I don't take my amvs as seriously, so I'm never hurt when someone doesn't like my videos.
However, critique, or just plain reactions, are the only reason I make amvs. It's not going to help me improve, but it's certainly going to drive me.
So typically, when I full on review something, I'm naming all the little things I see. I see these in my own amvs too, but unlike most people, to me they're important and also insignificant.
For instance: If I see an amv, I'm not watching for all the errors (unless it's blatantly obvious and I can't help it.) I watch it, and I enjoy it, don't, or have mixed feelings, whatever. On the other side, watching it again I see all these little things that could change. And me mentioning all these little things like I do isn't going to help the person. They're not going to go back and change their amv. And when they make a new, completely different amv, it's likely not going to help that either. Amvs are circumstantial, and therefore, so is critique. I could say something all-encompassing, like "watch your fades, there's too many," and maybe that'll help, but 90% of the time, I've never seen my critique help anybody.
Do you ever seen an amv released by an editor after you gave them previous critique on a video and say "Wow, they took my advice!" You think telling them that that fade was out of place or that cut was too abrupt helped them make an entirely different video? If you gave them some advice like "watch your transitions next time," not even that's going to help. Watch what? What do I do? What's wrong?
You know why that person got better? Probably because they watched amvs. Or they just kept on editing. Or maybe someone gave them some critique that wasn't too generic, but not too specific to be useless either. And a lot of the time, nowadays, it's because they had beta testers. But a critic who improves the editor is the one that doesn't make comments like most people on here do. I will say, there are some pretty good ones, and I think they might have helped improve an editor from their comments, if they chose to take that advice. But ehhhhh, most the time, most comments you see nowadays.?? no.
So the reason I do it is for myself mostly. I might like the editor and the video, so I'll give them something more in-depth, because it's better to get "long" comments, but in the end, it's most beneficial to me, the reviewer, rather than the editor, because it keeps my mind thinking "critically," as someone before mentioned (can't remember who, kinda just skimmed through the posts lol.)
Like I mentioned before, beta testers improve an editor the most, not critique that comes after the video is done. Myself, I've never sent out betas, unless I was in an MEP. I hate people beta-ing my videos, and I've never done it once in all the time I've been editing amvs. I don't like people telling me what's wrong in my amvs, because I know what's wrong, so your advice is useless to me. I've also never liked it, especially now, because I don't want people to change the way I edit. I want to edit things they way I first thought them to be. To me, that's original. Nobody's mind has thought of that amv but mine, nobody else would put together those same cuts as I did, or put those scenes back to back. And to have someone tell me to change that, I just can't do. I'd rather make a boring amv that no one liked. And I do do that a lot, but it's primarily because I'm lazy, like I mentioned before
And I also prefer to surprise people
I realize no one will agree with me on most of the points I made, but I don't feel like it's necessary for me to repeat views that are commonly held, and mine aren't, so there you go.
To answer some of the questions:
Is criticism of the creator always inappropriate?
Not at all. Criticizing an editor has nothing to do with their amv at all, but that doesn't mean it's not necessary either. I've never seen anyone say "this amv sucks, so u suck, go jump off a cliff" before. Unless they were trolling. But if their attitude is plain bad, why not? What's wrong with not holding back a little?

Just kidding, but not really.
There have been times when an amv was just so bad that my critique came off mean, because it just inspired so much passion within me so as to cause me to just rage all over their amv. Honestly though, if you're gunna get so butt hurt by someone
online over an
amv, then I don't see a problem with it at all. But in terms of helping the editor improve, being helpful.??? lol, no.
In what format should group criticism occur?
I like it when people just get together and talk about an amv, voice or IM, whatever. It just gets people thinking, lets people see the differences among how people view certain things, etc. It's just more thought-inducing to just talk simply about it.
Must a creator give permission for any given and specific type of criticism to occur, especially if the work is posted publicly?
In the end, it's not gunna matter, people can say whatever they want, you can't control them. If they say they aren't looking for certain critique, then I'll be the one to respect that, but in the end, people will do what they want.
Should criticism be anonymous?
Uh, no. In no case is anonymous criticism beneficial. It's also not
not beneficial, but there's no reason for it to be anonymous. It's the internet, being a person behind a username is secret enough. If anything, the creator should be anonymous, since it's the reviewers that tend to affect their reputation, not themselves. By releasing your amvs anonymously, people won't judge you for past comments, amvs, etc. But I don't really believe this should happen either, I think you should just own what you say.
However, in one case, sometimes you don't want to critique an amv harshly because it's your friend.

I don't really have a problem with that, but I always see comments like "Oh awesome job Shelly/Nana/EditorPerson"

and they're best friends. And I watch the amv and it's an obvious piece of shit, how can they not see it? I don't know, some people just blow my mind sometimes.
As for this whole "critical theory" stuff, I don't take amvs seriously enough to really consider that. I'm passionate about amvs, kinda, and I can get pretty serious because people are just stupid sometimes, or I just feel like being serious, but critical theory? Way beyond me haha. I say, just keep doing what you're doing. We're all fine with our small comments, or our stupidly detailed long ones, or our mean comments, blah blah. By all means, get together and discuss it things like this "theory", like we are here, but I don't feel like it's necessary to get wrapped up in it either (not that anybody is, but it's just too serious for my taste is all)