To correctly transfer large video files you must connect the phone in 'USB Mass Storage' mode (not MTP mode).
With the USB cable
disconnected, goto: -
1) Settings => Wireless and Network => USB Utilities.
2) Select 'Connect storage to PC'
3) Plug in USB cable.
4) Select 'Connect USB storage'.
5) Select 'OK'.
You will now be able to transfer and play large videos.
For corrupt files previously transferred in MTP mode, I found some software to fix them, however the demo version will only repair the first 50% of the file unless you pay the €29 for the full version, which then only allows 5 repairs.
The company is 'Grau GbR' and the software is called 'HD Video Repair Utility'...
It requires the corrupt file and a good file to compare and apply the correct header unique to your device.
Hope this helps...
PS I am in no way affiliated with Grau GbR and still have half a corrupt file so if anyone finds some software that is cheaper or even free, please post!