As far as I am aware there are no significant changes between MySQL versions and the native (to MySQL) protocols they use. The JConnector drivers are numbered by their JDBC spec version. So the 3.x drivers support the latest JDBC 3.0 specs.
This driver is a typr 4 (pure Java) driver so you should not encounter any issues with your OS. With an exception being that if your JVM is pre JDBC 3.0 then the driver would be too new for your VM. If that is the case you should be able to use a 2.x driver without issues.