I have seen this frequently on a server running XPages applications where Notes Objects are not being recycled properly. You should be able to search the server log for the text JVMDUMP to see if a dump occurred somewhere before the Error 500 started occurring. The only immediate solution I found was to restart the HTTP task which frequently ended up crashing Domino server which then had to be restarted itself.
The real solution is to be extremely conscientious to recycle ALL Note Objects in your Javascript (and presumably java) code in all XPages applications.
I have had to go back over (when I first started developing XPages apps) all of my XPages, Custom Controls, Javascript libraries and agents and find every instance where a Notes Object was created and recycle it when I'm through with it. Then because I was on a shared server, I still had problems because of other developers' apps who, presumably, did not recycle objects.
It is absolutely critical to recycle all Notes Objects in your Javascript code.