Allow users to uploading videos to vimeo
I don't believe uploading directly to Vimeo is a supported feature. I do see an unmaintained module that claims to do something similar, though: http://drupal.org/project/mm_vimeo

I haven't looked at the code, but you could write a module to accomplish the following:


Use a regular file upload field for videos. Nothing fancy. Use the Media module to enable URL video embedding (as if we've copied/pasted a Vimeo URL directly). 
Create a cron job to keep an eye on nodes created/updated of that type, making note of videos that should be uploaded to Vimeo. 
Upload videos to Vimeo (see: http://developer.vimeo.com/apis/advanced/methods#vimeo-videos-upload)
Modify the Video nodes to include a Vimeo URL to embed in the player. 
Remove the file upload, chances are it's huge and not worth retaining. 


I've used a modified approach with this in the past with transcoding services in conjunction with Amazon S3 storage and Cloudfront CDN hosting. Very good combo.