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#bottom isn’t showing up because it’s full of floated elements so it collapses on itself. Applying clearfix to bottom fixes your problem, but since you have head.gif it’s some sort of checkered background.
Well yes that’s true, overflow:hidden will cut absolutely positioned elements, or select boxes if they hang out of the #footer div. But it there will not be any of these, then I don’t see any problem using overflow:hidden as a clearfix solution.
As I mentioned, it’s not supported in older browsers, so if he’s looking to design with IE7 or lower in mind, it’s not the best solution..with THAT being said, your inline-block solution is no better, as inline-block was first supported in IE8 as well, in addition, the pseudo-element :after wasn’t supported until IE8 either