Forgot to say that a Mac shouldn't present any problems with importing, it's probably the way you've done it.
If your live server has PHPMyAdmin as its database admin facility, then do a dump (export) of the whole DB and then use MySQL Administrator to import it. I often find that the way that one tool exports the DB doesn't suit another tool when importing it.
If your live server allows you to use Sequel Pro to connect directly to it from your Mac, then export from your test server, close the window once done, connect to your live server and create a DB with exactly the same name, then import the SQL you just exported.
If that doesn't work, then it could simply be that your MySQL on your test server is newer than that on the live server, and there is some sort of incompatibility there... but I'd be guessing at that!