Short summary of the results
Overall, it's so nice that it even made me change my opinion about significant whitespace which I never liked before.
For the sake of simplicity, I just run up this script in a shell:
coffee -wc -o
It compiles the files in the CoffeeScript directory as soon as they are saved, and outputs errors, if any. Most of the time the errors are very easy to track down and fix.
For Rails apps, another option is to use the bistro_car gem to serve CoffeeScript. For Rails 3, there is also Barista.
Naturally, my IDE doesn't have any support for CoffeeScript beyond syntax highlighting. It would be nice to have built-in navigation, auto-complete and syntax checking, but so far my CoffeeScripts are simple enough that I can do just fine without these features.