Now thats an interesting idea...
First thought would be to add the version of the software into the hash as well. I keep meaning to write a catchall uncaught exception handler that displays the package then reraise the traceback (so I don't have to ask people what version when I get a random traceback).
Being able to do that, and also stamp the traceback with an id could be very handy. Especially with some bug-buddy/bugzilla/etc tweaking.
Of course, double fun would be way to go from the id to at least a rudimentary stack trace, but that would probabaly cause a large id.
But I suspect you could do something like enumerating all the methods, then just using that as the id, so you could get something like 1.0.0-1:1-23-37-111 indicating a stack of method 1, method 23, etc...
Keep around a list of the enumerated methods, and you could get a relatively useful idea where the error is. The method name-> number list could be autogenerated fairly easy I suspect.
Not sure how to handle anonymous methods and lambda's and friends though... Could probabaly just enumerate all the lambdas as well. Not perfect, but close enough.