Vimeo broke playback on all versions of Firefox several months ago.
They have implemented a work-around for Firefox v3.6, but all other versions of Firefox (older or newer) do not work.
The problem has been reported numerous times, but Vimeo still have not fixed it.
It's a Vimeo problem (although they tried to blame it on Firefox).
Vimeo made a change to the web site about 3 months ago and it broke video playback for all versions of Firefox. Later (after many complaints from users) Vimeo finally got round to putting a fix in place, but the fix only works for Firefox v3.6. Vimeo video is still broken for all other versions of Firefox (including FF 4.x).
Firefox 4 works perfectly fine with video from ANY site other than Vimeo (e.g. YouTube, Daily Motion, SmugMug, etc.) it's only Vimeo where video doesn't work in FF4.
It's clearly a Vimeo problem, but they won't take the issue seriously and fix it. Maybe not enough people have complained to Vimeo.
Problem has persisted through all recent Firefox releases: 4.x, 5.x, and now 6.0. Seriously, screw Vimeo.
And the first person who tells me to switch to that godawful Google Chrome BS gets a punch in the nuts.