It's got to be thick. I'm thinking rhinoceros-like. Maybe even armor-plated. Constructive criticism can sting the ego, but it's a gift. It gives you another perspective and forces you to make tough decisions that hopefully make your work better.
Unfortunately, some authors seem to be allergic to criticism of any kind. They go into literary anaphylactic shock at the first hint of it. I've got bad news, kids. If you think my feedback is rough, wait 'til you come up against agents and editors that won't even read as much as I did.
Here are some of my ideas of appropriate and inappropriate responses. Take note - considering feedback does not necessarily mean making changes.
Feedback: "This part is confusing."
Appropriate Reaction: Assuming this person is within my target audience and thus has the requisite background knowledge, I'd better check that part. Is something obvious to me because it's in my head, but it's not coming across clearly on the page?
Inappropriate Reaction: This person obviously has no idea what they're talking about. It's all there in black and white. How can they miss it?
Feedback: "This formatting choice is distracting."
Appropriate Reaction: Uh-oh. Last thing I want is for my readers to be distracted by something like format. Why did I choose to use italics/bold/double-quotes/single-quotes here? Can my purpose be served by something less obtrusive? It's only one person's opinion, so I'll keep this as a note to myself. If others comment on it, I might want to rethink it.
Inappropriate Reaction: This is what makes me distinctive. I don't want to look like every other book. If they think my use of reverse-indentation is hard to read, then they're just missing out on my genius.
Feedback: "I had a hard time getting into this."
Appropriate Reaction: Yikes. Is this person part of my target audience? If so, I need to figure out why I'm not drawing them in. If not, I should still consider my hooks and pacing, because it'd be nice to have broader appeal.
Inappropriate Reaction: How dare they attack the product of my blood, sweat, and tears?! Everyone else who's ever read this (i.e., all my friends and family) say it's the greatest thing since [insert name of favorite author here]. This person is clearly just mean-spirited and jealous of my massive talent, because otherwise, they wouldn't be able to drag themselves away from my pièce de résistance.
For the record, I'm only mildly exaggerating.
Good luck in the publishing industry, kids. See you around.
[ETA: Eight months after I posted this, Pete Morin blogged about rhinoceros hide. Check it out.]