78 levels? Wow
Thanks! I stored the levels in a way I found to be some what clever. They are all in a long string, while it bloats the class file it's still excellent to compress. My class file in uncompressed form is a whopping 10456 bytes, while the compressed jar is 4087 bytes [and it could probably be compressed a bit further using KZip].

Oh, and first level's much harder than lvl 2, by the way.
Yes it's hard to set the order correctly. From playing with friends I noticed that what was seen as easy for one person could be very hard for another, then on another level it was the other way around. I guess improvements still could be made in the level order, I'll save it for last.
Flickers alot when using the appletviewer... other than that it looks and works fine.
I got some flickering too, like it's tearing a little. Are you drawing straight to the Graphics or drawing to a back buffer first? Nice sokoban game though, good job!
[edit]: Got help with it from nonnus. No need to clutter the thread with the source code any more.
I solved 39, it flashed, then froze:
My friend told me the game froze upon clearing lvl 39, and that he started in the wall on lvl 40.
Ouch, bug!

Thanks for mentioning it. I have a feeling about what it is, I'll solve it tonight.