Well, it really should happen, "Whose Realm, His Religion" (or however the Peace of Augusburg (1555) went), so the HRE really should get a very special role in this game, and it would be cool to show certain events unique to certain civilizations like Pepin's defense of Rome from the Barbarians, or the investure crisis between the HRE and the Pope; and of course the Great Schism, forming two Popes in Avignon and in Rome. These are central events which are missing, and I think this is especially due to the fact that the HRE is not properly represented, and if you can, having "no-state" religion would probably be best (it could be the German UP, that with "no-state religion" you get a certain happiness bonus or whatever).
Also why did you guys leave out Prussia?
And finally, please add 1-2 more Islamic Missionaries to the Ottoman spawn, (I hope this dosen't make me sound like an "online" jihadist

) I don't know if this has been fixed in Beta 4, but it was a problem earlier. Or even better, I would recommend having Islam just roll over Anatolia, kind of like it does in SoI, where it is programmed to spread during the Turkish invasions.
And upping the Sultanate of Rum horse archer invasions of the center of Byzantium would be good, as currently I feel its too easy to defend from them.
I'll talk about the Crusades later, once I actually get around to playing Beta 4
But good job so far, I like the changes made in Beta 4, especially now that England will capture Dublin