Well, they're right about the section breaks. They have too many uses in Word, and one of those uses is "switch back and forth between one-column and two-column layout on the same page." That kind of Word-formatting needs the Will-treatment (forensic reconstruction in InDesign) because there is no way to automagically transform Word-garbage into InDesign's document-layout model.
Regarding nonbreaking spaces, they're full of it. Nonbreaking hyphens are a different story; the links I posted in my first response tell that story. A bit of pre-import hygiene in Word will save you a lot of headache in InDesign. But nonbreaking spaces? Whack control+shift+spacebar in Word, get a correctly-encoded valid-in-Unicode no-break space. It survives infinite Word -> InDesign -> Word roundtrips undamaged.
Footnotes? Hollow laugh! I usually set mine up manually, but I don't have to handle them often. There are other forums regulars who might happen by with some words of advice and/or consolation. I think your "experts" are wrong when they say don't import; they simply don't import well. It's a hassle.
Word formatting interfering with 508 compliance: Yup, it's a hassle. But you are correct in that most of the source is in bad practice within Word. If there are 700 of you, some training is in order. Carefully groomed normal.dot files (imposed from above by your IT folk) might be helpful here. You can do things like prevent local formatting by locking down the document, too.