The Facebook app is probably the fastest way to find a list of all permissions in the Android system. "Draw over other apps", "Read battery statistics". I don't know what part of facebook requires either of those options, and the mobile version of their website offers me the minimal amount of functionality I need.
The act of writing this comment has made me uninstall the damned thing. Just reclaimed 17.61MB, and probably a fair amount of space in my mind since I'll check Facebook less often.
I'm sure, as the author of the linked article asserts, most people blindly accept the permissioning changes, but I hope this permission-creep starts to cost them installs.