I have applied movie texture to screen of TV. Its working fine in editor but when I build and run unable to see video.
We ran into this as well. Not with Unity5, but with 4.6x.
I am not sure if this would be relevant to your case, but the results changed when we lowered the screen resolution.
Ultimately, I tracked the issue down to some weirdness with the use of Playmaker and Canvas to play movies. We had another movie that used the old method inside OnGUI, and so I got rid of the Playmaker/Canvas method of movie playback and used GUI.DrawTexture, instead.