Isn't the Real Name policy a bit of a joke? I have a few test/fake/dev accounts, never had any issues (but for new accounts, need to associate them with a mobile number, but only for the initial signup).
That said, I think the structure of Facebook intentionally makes it difficult to moderate. Reddit, for example, has public groups, group mods, etc. Far from perfect, but Facebook could definitely do more validation before promoting groups.
Funny, last time I changed my birthday on Facebook I was asked "Are you sure? You can change your birthdate at most 5 times". Presumably they must be aware that at least one of the birthdates I gave was false.
That said, I think the structure of Facebook intentionally makes it difficult to moderate. Reddit, for example, has public groups, group mods, etc. Far from perfect, but Facebook could definitely do more validation before promoting groups.