can you continue playing after you beat kh2

You probably have a defective disc. Check it for scratches.

 

DX Get the disk cleaned. DX DX DX & the sad part is: YOU CAN'T CONTINUE PLAYING AFTER YOU BEAT KH2! After they show you your battle report after the end of the game & credits, you won't be able to continue & you definitely won't be able to do the L2,L1, R2,R1, Select, Start buttons to restart the game either, so you have to end up walking to the PS2 & press the restart button on there. DX

 

Well KH2 is Square Enix and they discarded the "secret" SqaureSOFT soft reset buttons.

To answer your question, sora978.
After beating Final Xemnas, you get the Cut Scene with Riku and Sora somehow making their way back to Destiny Islands where Kairi, Mickey, Donald and Goofy are waiting after the Sora and Riku Cut Scene.
Then Rolling credits while listening to SANCTUARY-After the Battle (if you have the English KH) or Passion-After the Battle (if you have the Japanese version or FM+).
You wait, and then a hint of perhaps another KH Story involving Sora (it's not Coded, most likely "KH3")cut scene.
Then depending on how you played, you will get the BBS Teaser.
Then it goes blank and shows your battle report. You cannot do anything but look at your battle report and listen to Dearly Beloved repeating itself.
You cannot continue afterwards
There is no New Game+ or anything like that.

And yes, it seems your disc is damaged.

EDIT
The songs I put in the Rolling Credits could be wrong...
It might be the Kingdom Orchestra Instrumental version instead or perhaps as well =]

 

Yeah, your disc is probably defective like everyone else says. And like rawr says after you beat Xemnas you view sora and riku sitting on the beach from gthe beginning of the game in the darkness, most likey a dark version of destiny islands(i'm assuming...). sora receives the bottle kairi left floating on the ocean and opens the door to light returning to destiny islands where kairi patiently awaited their return. They receive a message from the king sometime later and set off, i have not fully beaten kingdom hearts 2, but i'm pretty damn close. but i do know if you complete a good portion of it you get a trailer for what looks like birth by sleep for the psp, it deals with the keyblade war and the original keybladers: Aqua,Terra and Ven(who looks suprisingly like roxas.)