Emergency contact - Apple should add a second swipe on lock screen- one for the 911 call and one for your emergency contact. So they can call spouse/parents etc without having to unlock phone
Why can't they have one extra thing on the page where you can make the emergency phone call? You should be able to dial 911... But also to make that emergency contact call so the police can call your spouse without breaking into your phone. Or even if you lose your phone and an actual nice person, or good samaritan, could call your contact and tell them they have the phone.
iPhone 6 Plus, iOS 8.3