If you do a quick search of the Android Forums, a general complaint is just the performance of it while Facebook runs in the background as a service (impacting the currently used app) . Also tends to be a battery hog from all the syncing it does. I don't want to get into the whole privacy debate on it, so I'll let someone else field that part.

However, Android Permissions are "all or nothing" when you install an app. Combined with apps being able to potentially access much more than other platforms based on the permissions an app requires (as well as any app can read your sdcard without permission prior to Android 4.1 [though it's still disabled by default on 4.1 so apps not accounting for that permission don't crash]) and the need of some people to install certain apps, they must choose what is more important--potentially giving into whatever permissions this app wants or doing without.

I don't personally use it because I don't want Facebook on my rooted Android device (though I'm like that for most apps), but I have seen those reoccurring complaints over the last few years.