I\'m not a Windows Phone developer, and I want as little to do as possible with anything related to Microsoft. Nonetheless, I need to get my mobile web app running properly
Unless you have a Windows Phone 7 device, you will need to run Windows in BootCamp and install the Windows Phone Developer Tools in order to test in IE on the emulator. I don't know about Whine, but I ran into major problems trying to test in Parallels - so based on my experience, I suggest keeping it as simple as possible.
There is no console in IE on the phone, so you will need to use alert, like you suggested, or just write text to a div on your page as a custom console.
If you really want to code in OS X (which I definitely understand), using a separate machine for testing IE in the WP7 emulator is going to be your best bet.
EDIT: I just tested alert and it did work fine on my Windows Phone. My guess is that a syntax error is preventing it from calling.