Sounds like a text encoding issue. Mobi only deals with utf-8 or windows-1252, I believe.
Then I validate it EPUB Validator. Everything is fine on my kindle.
This, however, confuses me. The one has nothing to do with the other (unless you're talking about a third-party ePub-reading app on a Kindle Fire). Convert your ePub with the official Amazon tools (kindlegen/Kindle Previewer) and see if the "squares" don't go away.