I have found I can no longer delete individual text messages by tapping and holding a message, choosing More and then the little trash can appears. That trash can no longer appears, and the only option I have is Delete All, which I picked once because I assumed it must mean Delete Selected also and I lost the whole text conversation, of course.
I have checked with an IT colleague who has iOS 8 on her iPhone 5S and she still has the little trash can option for individual selected texts, so it must be an iPhone 6 issue. If anyone knows anything I would be pleased to find out, because I have only been able to find two other posts online about it and all they keep getting is people saying 'hold text and select More and chose little trash can'. It doesn't appear on iPhone 6, just a camera icon on one side and Send on the other.
Edit: apparently, restarting brings back trash can. Unbelievable. Leaving this post though because I saw several others ask about this elsewhere.