Actually … the blogs.dir part isn’t used except for internally.
Let’s say you have a network with two sites – http://url.com and http://sub.url.com. The files will be located in (respectively):
http://url.com/files/2011/06/...http://sub.url.com/files/2011/06/...
The blogs.dir directory is where the images exist physically, yes, but your .htaccess file is routing the virtual directories I just listed above to the correct location.
I’m guessing you’re manually putting together the URLs you reference above … because that’s not how Multisite is set up to work by default.
Update
I just tested this on my own network installation to give you a specific example.
My main blog is http://mindsharestrategy.com (custom domain mapped to a subdomain network installation – http://business.eamann.com is the same site). A recent post with images: How to Publish a WordPress Plugin – Subversion.
The first image in the post is: http://mindsharestrategy.com/files/2011/05/checkout.png
But an alternate link that also works: http://eamann.com/wp-content/blogs.dir/2/files/2011/05/checkout.png
WordPress automatically maps the /files directory for this site to /wp-content/blogs.dir/2/files via the .htaccess file.
So your image permalinks will work with the shortened version … there’s nothing you need to do there. It sounds like your problem is actually with the way the shortcode outputs content.