Do not download any software to do this! Just follow these steps. 
1. replace the www in the URL with m. e.g. http://www.facebook.com/blahblah - http://m.facebook.com/blahblah
2. this brings you to the FB mobile site, once there click on your video. 
3. While the video is playing if you are on a pc right click on the video screen and select "save video as" (sorry cant help the mac and linux folks out there) and pic a location on your pc to save the video.