iPad Air also freezes lots with 7.1.1
iPad Air with the recent 7.1.1 update has this issue as well.
Unfortunately, many times starting up an app freezes on its opening screen. Double-clicking the home button, swiping up to pick from current apps, even clicking the Wake/Sleep buttonall these actions do nothing. (I think I hold the Sleep button for a while, and then the iPad returns to the Springboard (the "finder").)
Just now, I opened the Apple cover on my iPad Air (which should wake it immediately) and was greeted by a black screen. Holding the Wake/Sleep button did nothing. I finally had to Reset by holding Home and Sleep for 10+ seconds, and that worked to turn on my iPad Air.
I would hope that Apple is working on a fast patch to this awful problem.