I wasn't aware that's how it worked for the vanity urls. It's a pretty ugly way of handling things but probably the only way they could do it without writing their own Url Rewriting module. The problem with going down this route (as you've found out) is that it solves one set of problems but can create a whole other set if the web server isn't configured exactly the same way as the developers might have expected.
The problem will be that you have (I assume?) switched on extensionless URls and mapped all requests (wildcard mapped) to the asp.net runtime. I'm also guessing that what this does is send all 404 errors to the 404.aspx handler provided with AS, and this is causing the above exceptions.
The first thing to do is to check why these particular requests are resulting in 404 errors : does the /portals/default/skins/weezkids_new/dnnmodules.css file exist? You could either create the file or remove the reference to it in your skin.
I would also assume that you have the standard 'ignoreRegex' filter in place for Url Master, and that it ignores both .css and .ico files. The problem being is that even if the rewriter ignores them, perhaps the AS 404 handler is not expecting that. I'm not really sure, I'm only guessing and so I need some more information.
Can you:
a) check to see if those files really don't exist
b) see if deactivating the AS 404 handler changes/removes the error (I'm not suggesting to remove it permanently, I just want to see how it affects things)