I'm not sure if converting upon selection of another font would actually be desirable. If you would select the original font back you would get gibberish. Unless Word would re-convert the Unicode char back into whatever similar character the selected font would offer, and that is of course prone to errors.

Word used to rely heavily on things like the symbol font to create out-of-ASCII characters. IE still supports this. I would not like Word to think for me and convert things automatically, it does that far too often already.

I do agree though that it is desirable to, at some point, convert all non-Unicode characters to Unicode. In a deliberate action, not an automatic one.

One thing you could try is a find-and-replace action. Using the styles list, you can select all text sections with a specific formatting (for example: normal + font:symbol). Go to the fist one, and find-and-replace that character/text section with the desired Unicode equivalent in the entire document. Repeat until no text in that font exists anymore.

It takes a bit of effort, but certainly not as much as retyping the whole document.

Alternatively, save to HTML and search-and-replace with a text replace tool such as text crawler.