@teet: this is a different issue since you try to use rounded corners on an image, which is a known problem in various browsers.
@chrisjb: As for Nicehair.org: I’m thinking it might have something to do with the media query. You’ve set the breakpoint at exactly 768 pixels (if lower than that, don’t use rounded corners) and I think it’s not taking it well. Check the layout on an iPad and on a browser that has a 768 width, it’s different.
Things you might want to try:
Add this line in your header, or experiment with some of those values:
Or, instead of max-width in your media query, use max-device-width.