Ah well. I've never found out what this behavior is triggered by, but it seems very persistent: at work I have several different versions of Word, but a file that's “broken” cannot be made to work by re-saving in any other version. That encompasses saving as .doc, .docx, and .rtf — if the file is broken, it'll stay broken. Let's hear a Yay! for Word's persistent Backwards-Compatible objects.
Once or twice I got so fed up I saved the file as .rtf and opened and then re-saved it with WordPad. Now that's a sure-fire way of expunging every single nasty bit from a file! It's just too bad some of the 'good' stuff goes along with it … You can realistically only do this with files that are plain text to begin with.
By the way, most — unfortunately, not all! — Word files with issues import just fine into CS3. If you have one of these lying around, import the text in there, save, open in CS4 / CS5 / CS6 (hypothetically), then copy the text out of it into the target document.