I'm guessing because I don't have a smart phone or video capable MP3 player.
But videos need codecs, (CoDec = Compression/Decompression) software that compresses videos to a more manageable size then decompresses it when being played. The incorrect codec can cause the problem you have seen, a mismatch in video and audio.
I assume that different mp4 videos have been compressed by different codec software, (it is the mp4 maker's choice), and so any player that plays mp4's must have the same codec installed.
It's easy on a PC as we can download and install all sorts of different codecs, or use player software like the VLC Player for Windows that has its own codecs installed. But I have no idea how mp3/mp4 players manage this.
The test would be to check the videos on the device you transferred them from, (I assume a PC), with a codec utility like GSpot Codec Information Appliance to see what codecs each of these videos use.
However, I note you said you loaded one mp4 and it played correctly, but then others you loaded do not. What happens if you remove them all, then try one at a time?
Mark