At the moment we are running the latest Moodle Build V2.3.3. I have setup a videos using the build-in moodle media Option, one embedded video and one linked drectly to the video file. I will also setup one Video using JW Player, so you can see the diffrence. The video I'm using is a normal mp4 but I will encode it to a m4v and test again. If you want to login to our Dev Site, please send me a message directly and i will send you the link and user details.
Moodle for mobile
I think the best would be to export your videos to FLV extension as Flow player pretty much handles that the best.
Don't blame Moodle for mp4/m4v files because HTML5 is not supported the same on all browsers. I know that IE9 doesn't support HTML5 at all.
You'd have to hope that all of your students have quicktime installed and that's a hassle. So take your mp4 and run them through anyvideoconverter (http://www.any-video-converter.com/download-avc-free.php) this will convert them to FLV.