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Alas, Firebug isn't available for IE. There are a few "for pay" tools that are supposed to be similar, but I haven't been able to see to my satisfaction what I'd get for my money. I also understand that Visual Studio has good tools.
When I was at Add On Con last week, Joshua Allen from Microsoft said that you should develop in IE8 because it has the best developer tools. I found that to be true--although they still leave a lot to be desired compared the Firefox.
The first thing you have to do is turn on debugging in IE by making sure that the "Disable script debugging" options are unchecked.
The error messages you get are pretty cryptic, but they at least give you a clue about where to look. The worst part is that they don't give you the name of the file where the error occurred. Ugh. @whitmer suggested Companion JS (not free for commercial use). I haven't tried it, but it looks like its a step above the stock debug messages.
So far, that's what I've discovered. I'm sure there are better ways and tools. I look forward to someone educating me.