If you allow remote MySQL connections, you need to use a whitelist with a default deny configuration. Allowing remote connections only from trusted hosts does not present as large of a security threat as the community seems to believe, but nevertheless, it does increase risk, mainly in the event that an allowed host is compromised by a malicious third party.
If remote connections are used only for a specific and limited purpose, then the best solution is to use a PHP or perl script to process requests from that host, and make appropriate database changes through that script. This prevents a comprimise of a remote system from giving the attacker full control over a MySQL user account. In addition, SSL can be used between the remote system and the main database when making HTTP transactions; this prevents the (unlikely) problem of a malicious user capturing traffic as it passes from one datacenter to the next.
