Recorded video visible on device, but not other media players once uploaded
MP4 is a container that can contain different video codecs, it sounds like your device is creating its videos using an unusual codec that not many other devices have loaded by default. As Seth and Hcpl have said VLC Player can play almost any format and should be able to play your videos.

If you want to know what codec is being used, then try opening the video in a codec identifying app like GSpot, this should tell you exactly which audio and video formats and codecs are in your videos.