I've used Flowplayer with all my WP themes (both free and homemade). When I purchased my first premium WP theme, it warned me that it was compatible only with YouTube and Vimeo, but I wasn't worried.
I tried WP's built-in player, but it didn't work on mobile. I installed Flowplayer 5 from their web site, but it didn't work with the theme. I installed the "official" Flowplayer 5 WP plugin, and wouldn't play Mp4s on mobile. Thank goodness, the FV plugin worked, and the only sacrifice I had to make was switching to webm files!
