See my comment here
It's a known issue with Mac OS. Essentially the applet can't own the context it is drawing to, because the JVM plugin now runs in a separate process. To get around this it does some copy/update magic, but the downside is that applications that update constantly (like games), flicker horribly. You can drag the applet out into it's own window (I don't know specifically how, as I don't use Mac OS, but you can), where it owns the Window, and so avoids the copy/update issue.
Other OS's are unaffected because Mac OS has a more restrictive security policy around window ownership between processes. I believe on Mac OS they have to be explicitly given from one process to another, which browser's currently aren't built to do.
I believe the 32-bit JRE is unaffected, as the JVM doesn't run in a separate process; this is simply because it is out dated. But these days most browsers will use the 64-bit JRE by default (I believe you can only get 64-bit on Lion), and some browsers will only use the 64-bit version (if I remember correctly, Chrome does this).