Actually, it's a bug in the JVM.
However, regarding CLASSPATHs, Eclipse supports all sorts of classpaths, each of which may be independent of the other. Most of them are in custom build (e.g.
Ant) and test/run profiles, but the model for them comes from your project's classpath.
On the Java Perspective:
Right-click on the project, select Properties and in the Project Properties dialog, select "Java Build Path" and the "Libraries" tab. Click on the "Add External JAR" button and aim it at your mysql driver jar.
If you do that, when you select Run or Debug, the model project will include the database driver when it builds a default run profile. Or you can skip all that and simply create a new run/debug profile and do the equivalent of the above directly to the new profile.
You would only actually
need to include the mysql driver jar in the actual project itself if you were casting to MySQL-specific objects and the live code compiler needed those class definitions.