“Proper quote marks” I think — and also proper long dashes — make the web a more beautiful place. You don't even need any special software to use them since most programs and web services now use Unicode and just allow you to type the character and then display, store, and transmit it correctly.
Internet Explorer before version 5.0 always displays soft hypens. That's terrible, but IE version ≤ 5 are virtually extinct now, so the problem is less. IE ≥5.0, Firefox ≥3.0, Opera ≥9.0.2, Safari ≥2, and even Lynx ≥2.8.2 all treat soft hyphens correctly, while those other browsers who don't support them will just ignore them. (Source: )
Google and other major search engines correctly ignore soft hyphens. (Same source)
In other words: soft hyphens are safe and beneficial to use as of now.