Whenever you authorise an app on Facebook, you have to grant it certain permissions. The problem with Facebook's new app centre is that it uses a few design tricks that effectively minimise or hide those permissions, so you're encouraged to allow apps without really thinking about them.
TechCrunch has highlighted five of these design tricks in the "improved" Facebook app centre, comparing the old design with the new one.
The first example shows the old Facebook using two buttons "Allow" and "Don't Allow", while the new one offers just one button -- keeping users from thinking about the choice.
Similarly, instead of a bold black font detailing the permissions apps are requiring, now they are in tiny grey fonts:
Facebook designers know that you are used to ignoring those grey texts on the page. You're practically conditioned to think that grey text = unimportant. This is why they chose grey for the permissions you're about to grant.
Check out the whole post on TechCrunch for more eye-opening examples of these tricks.
Just knowing about them can help you become more aware of the hidden permissions. If you want more control over your Facebook app permissions, see previously mentioned extension FBSecure or also highlighted fPrivacy. These will make the permissions not only more apparent, but also let you choose which ones to enable or reject.