I know Apple completely bombed HTML5 video support for iOS8 homescreen web applications with no way to fix them. For those who don't know, it nukes the web application when attempting playback.
Currently: iOS 8 - iOS 8.1.3 has broken HTML5 video playback for homescreen apps.
EDIT 1: Thank you villecoder for confirming that it 8.1.1 is still broken. I'll update the question when 8.2 gets released.
EDIT 2: As 8.1.2 only fixes issues with ringtones, it's still marked as broken.
EDIT 3: Tested against 8.1.3 on an iPad Air 2, it's still broken.
EDIT 4: Still broken in iOS 8.2
EDIT 5: HOLY COW WORKING IN iOS 8.3