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I got this answer at developer.facebook.com:
Replace the word page with profile and it will work. Your new statement will be:
[[UIApplication sharedApplication] openURL:[NSURL URLWithString:@"fb://profile/247377102029332"]];
Same problem here. fb://page/PAGE_ID is not working anymore. Note that fb://profile/(fbid) wasn't working properly on Facebook 4.x returning a "corrupted" page in both iPad and iPhone. Instead, fb://profile/(fbid)/wall in Facebook 4.x worked well when using an iPad but didn't work with an iPhone.
fb://page/PAGE_ID was the only option that worked on both iPhone and iPad, based on my experience.
I used to use http://wiki.akosma.com/IPhone_URL_Schemes as reference, but it's currently down...