I created a small sketch on my Mac (OS X 10.7.4, Java from Apple fully upgraded), and then exported it as an applet. When I load the index.html in Firefox (14.0.1) the sketch runs nicely.
If I load the index.html with Safari (6.0), however, only the text that should appear below the applet is shown at the top of the page. There isn't even an outline where the applet should be. The Java console doesn't show anything (and isn't opened in the first place), so it seems safari doesn't even load the applet.
Execution of Java applets is enabled both in the general Java preferences and in Safari itself.
It seems there has been another post addressing this (or a similar) issue more than a year ago but got no answer.
Can you load other applets (non-Processing) in Safari? For example, this one: http://cs.smith.edu/~thiebaut/java/sort/ (This kind of problems is, alas, why support for applets is dropped in Processing 2.0...)
Well, applets are made to be seen on the Web, so the Safari glitch isn't really important for local files. Now, if you want an easy / fast way to check your export, beside using something else than Safari, you can install Apache and put the result of the export to the www (or whatever it is called) folder. You can then see the applet via http://localhost/yourApplet