How to play videos in HD on youtube.com in Safari on iPhone 6
Workaround: Use the desktop site, here is how:


In mobile Safari, find the clip that you want to watch, it will
initially start in low resolution.
Tap the address bar.
Swipe down in the page and you should see Request Desktop Site,
tap it. Sometimes this may open the clip in the YouTube app on the first attempt, try again!
On the second attempt it may ask you to open in YouTube app, don't
allow!
On the third attempt you should see the Desktop version of YouTube.
Tap inside the video to start playing in HD, sometimes you need to tap a second time.


Note: on my iPhone 4s iOS 8.1.2 the Desktop version of YouTube is much slower, unresponsive and harder to use. But since YouTube app can't play any videos over AirPlay, I had to find alternatives.