I have just set up a new solution / project to test this out (using the latest azure sdk as of 10/9/2012). I started with Cassette to try to minify, compress, and combine my css and script files. When running locally I get a 500 error when trying to access my page. Oddly I can not get more information even if turning off custom errors, turning on debug etc. I then uninstalled Cassette and tried Combres (someone said they had made it work with Azure). Same error. Just for kicks I changed my startup project to the web role only and low and behold the page loads just fine.
What setting am I missing to make this working web site work under Azure?
Edit: The page loads correctly (locally running on Azure emulator) when I remove any of the packages that would provide minfying/combining capabilities.
I had a similar problem with errors deploying to Azure. My issue was that a .less file I was using wasn't included in the .cspkg. You can investigate the packages to be deployed to Azure to ensure they contain all the relevant files.
In my case changing the "Build Action" of the .less file to be "Content" made everything just work.
If you enable remote errors for debugging deployment to staging the error should become obvious
<customErrors mode="Off" />