When I collect the stars in a session, they show up as being collected in the level select as desired. When I restart the game, they (often) disappear. So far only one star has stayed, and it seems to be there consistently.

Playing on Windows 7 64 bit, Normal mode.

Also, sometimes the game bugs out when selecting the final world - once selected once in a session, other worlds sometimes play the final world's starting slideshow. Also, it has crashed after selecting the final world before.