Recently, I noticed that Vimeo does not work anymore with the Flashblock Firefox Add-on: the play button shows up, but pressing it does not give you video during playback (even though audio works). I was using Firefox 27.0.1 under Windows 7 when I first noticed it and did not check it under Linux yet.
There are some discussions on this at the Vimeo forums, but at the moment the only solution is to disable Flashblock — on the Vimeo website only of course.
This is how you fix it:
In Firefox, go to Tools -> Add-ons. Select Extensions, then choose Flashblock on the right. Click Options and under the Whitelist tab, add vimeo.com to the list. This fixed it.
Here is a screenshot of the prodedure:##