Installing the plugin PJW Mime Config gives you a new options page –
Options > Mime-types – which allows you to add/delete the extra mime-types.
Adding a File Extension “webm” with the Associated Mime Type “video/webm” solves the webm upload problem.
I hope the WordPress team adds video/webm as an accepted mime type to core in future versions of WordPress. I guess we’ll see a steep growth in usage with Googles marketing force behind the format.