Just tried to do the check in through the app on my iPhone 4S. The pages are not fit on the iPhone screen. A lot of sideway/up-down scrolling needed. And in the end you cannot load the boarding pass into Passbook. Absolutely useless.
Guys from KLM: if you want to see how an app should function to and check the Lufthansa app (for iPhone and iPad)! Works flawlessly.
uukrae about KLM - Book a flight, v5.3