This is a short story I want to put down for those who face the same problem.
Several days ago I got a bug report related to list deletion operation in Checkvist - Internet Explorer showed a couple of alert error dialogs. The problem was intermittent on the production server, and I couldn't reproduce it locally at all.
Really nice and cool development tools in IE8 couldn't help me. I've had an exception object in my error handler, but there is no way to obtain stacktrace from it and find out where the real problem occurred.
I tried to rethrow the caught exception so IE would show me what happened - no luck.
To solve the problem I had to remove all try/catch blocks from Prototype's AJAX code, put it to the staging server, spend another 10 minutes to reproduce the problem, and - voila! - got an invitation dialog from IE8 to debug the uncaught error.
That was it. The error was fixed, Prototype was reverted to original state, code put to the production.
If you know another solution for the problem - please comment, I'd be glad to know.