No, there's nothing wrong with doing that, and yes, there's a product that handles it. Unfortunately it's a Windows program, but it's a truly excellent product. I use Dreamweaver MX 2004; it's one of the few Windows apps that are "must have" for now, until a good Linux alternative comes along. Dreamweaver handles all links when you move or rename a file -- or a whole folder -- beautifully.
Before Dreamweaver I used Allaire HomeSite, and it had a very flexible multi-file find and replace utility. With that you could, for example, replace all instances of "src='logo.png'" with "src='/image_dir/logo.png'" if you were shuffling all your graphics into /image_dir.
(BTW, Macromedia and Allaire merged, and HomeSite is now the Code View of Dreamweaver.)
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