This week I had to modify a lot of jQuery code to get it working with that horrible browser from Redmond. And the job is even harder without a tool like Firebug. Internet Explorer just spits a line number when there's an error, often without a file name, or just cryptic messages.
I refuse to install any other Microsoft application just to debug their errors, I prefer thinking, changing some code and seeing if line numbers change. It's a very old fashion way of debugging but it works.
One of the problems I found while working with Internet Explorer and jQuery involved using the html() method to change some element's content. I was able to solve this by modifying some parent() or even using remove() and then append() or after() (see jQuery docs). However, I haven't found any logic for most of these issues yet, in some cases html() worked but quite often Internet Explorer died showing a run time error.
Also, while designing a jQuery enabled calendar using an HTML table I realized that correctly using thead and tbody could make a difference. It's better to have a correctly structured table to avoid Internet Explorer complaining.
Making your web application run with Internet Explorer is not an impossible task but takes a good amount of time and can make you think about killing yourself while listening to a Steve Ballmer interview, yeah, that horrible.
I guess that many web developers, like myself, are already thinking on increasing their fees when some job requires dealing with Internet Explorer, not a bad idea, really.