Ok, did some further experimentation.
The same movie plays perfectly on:
My iMac (OS X), 13" MBP (OS X), iPhone 5S, iPad 2, iPad Mini, 2 AppleTVs
It will NOT play on the iMac (Windows 7) or the MacBook Pro (Windows 7) using iTunes 11.1.1
The two machines CAN play the same .m4v file outside of iTunes (using VLC) perfectly.
The problem is absoutely iTunes.