tried plugging it into your TV? I know in my case I have a panasonic plasma and panasonic bluray (both same year model) and although the blu ray player box sprouted about how many files it could play, I found my TV does more! The blu ray just seems too fussy. Sometimes yes for the vid, but no for the audio side of it.
But there is differences for files within a container like Mp4 etc. Maybe the files which have been encoded slightly different to the ones that your player does handle might be the key. I sometimes have this problem on both my TV and blu ray player. Even though it's MP4, it still doesn't work. If it's worth redoing I usually run it through handbrake and that seems to fix it.
As for the skipping, Does your TV or player have an SD socket? I have done this many times and find it works well, (with a good card) either that or I usually stream 99% from my media player straight to the TV via network cable.


