I've heard the language argument before and discounted it because Peter probably drew from Paul's superior educational background and learned. What historical and geographical facts indicate it was not written by Peter?
The "strangers" (exiles) in those areas were not there when Peter was alive in the mid 60's of the 1st century.
Those are areas that Paul has already evangelized. It does not necessarily indicate "exiles". It can very well be understood to mean strangers to the world at large because they have become Christians.
"Πέτρος ἀπόστολος Ἰησοῦ Χριστοῦ ἐκλεκτοῖς παρεπιδήμοις διασπορᾶς Πόντου, Γαλατίας, Καππαδοκίας, Ἀσίας, καὶ Βιθυνίας," The bold face words speak of chosen people (or chosen or elect people who are passing through, not really strangers which is another word) in a diaspora which in Greek implies exile. The Greek is beautiful. That alone makes me doubt that the Apostle Peter wrote it. Add to it Kosta's idea that the author is writing to people fleeing a persecution and it seems even less likely that +Peter is the author. Of course, to me that makes little difference.
Historical evidence shows early Christianity split between Peter and Paul. The two didn't get along theologically. I doubt that +Peter learned any Greek from +Paul. +Paul was in present-day Turkey and Greece. Peter was nowhere near.
The Jews living in Asia Minor and Greece when +Paul was there were not exiles. There were exiles when wide-spread anti-Christian persecutions began at the end of the 1st century. The Cappadocian Christians dug up a whole city in the mountains where they were hiding.
The Greek text of 1 Peter uses the word διασπορᾶς (diasporas), from which the English word "diaspora" is derived, which means scattering, exile. It is the same word used in the Greek Bible for the Babylonian exile of the Jews.
Surely you don't mean to imply that the Jews who left Israel 500 BC were still "exiles" in Alexandria and Cappadocia! The new exiles 1 Peter speaks of are those contemporary of the author's time.
And when +Peter was alive (c 65 AD) there was no exile#151;yet! The Temple was to stand another 5 years at the time of +Peter's martyrdom. The Jews began to leave Palestine after the destruction of the Temple (70 AD).
But, I agree with Kolo, it doesn't matter to me who wrote it. 1 Pet was chosen by the Church as scripture. That means that in it is God's message, according to the teaching of Christ.
Kolo says (#5058) The Greek [of 1 Peter] is beautiful. That alone makes me doubt that the Apostle Peter wrote it. Add to it Kosta's idea that the author is writing to people fleeing a persecution and it seems even less likely that +Peter is the author. Of course, to me that makes little difference
Indeed, it is ranked higher than that of +Paul's koine Greek! But, as you say, it makes very little difference if +Peter wrote it or not. The Church found it to be scripture because it contains God's message according to the teaching of our Lord.