Debugging Remote JavaScript

A newly added, not-quite-wanted function of my job is remotely
debugging JavaScript errors on other people's web applications. I have
tried finding a JavaScript debugger that would allow me to do that, but
other the Microsoft Script Debugger, I couldn't find any other.

Are there such programs? Basically, what I'd like to be able to do is
trace commands step by step and view the values of certain variables.

I was unable to figure out how to get Microsoft Script Debugger to
work. I read the documentation and executed it, but I keep getting
"Syntax error" messages whenever I want to see the value of a variable.
Add to that the fact that I am not a developer and I do not know
JavaScript (other than to read it, which is enough for me to figure out
what the problem is) and you see my problem.

I have read about the option of adding message boxes all over the
place, but this would not work out for me either, since I would need to
make changes to this code on the web server, where I don't have access,
and it would be a lot more tedious.

For those skeptical as to why I still expect to be able to debug
problems:

The problems are caused in most cases by the proxy we add on their web
servers, and they are due to values being changed on the fly. I only
need to find out where the code breaks and read the values of the
variables, which gives me the solution ("do not change this variable").