Discussion on the authorship and date of 2 Peter is wide-ranging and inconclusive. The epistle opens with the author's claim to be "Simeon Peter, an apostle and servant of Jesus Christ" (1:1). At this point it must be noted that "Simeon" is not a form commonly used elsewhere, and not used in the equivalent opening address of 1 Peter. Note also that it is more likely that Peter would use the original form of his name than an imitator, as an imitator would simply have copied the form used in the earlier epistle.
Throughout the letter, the author plainly identifies himself as Peter the Apostle, and claims several parts of the Apostle’s life as his own. For example, the previously mentioned introduction: 'apostle and servant of Jesus' (1:1); and the indications that he was a friend of Paul (3:15), that he was a witness to the transfiguration (1:16-18), and that he had previously written a letter to the same recipients (3:1).
While it is clear that 1 and 2 Peter have different styles (which could be explained with the use of a secretary [or secretaries] for one or both of the letters) the real opposition to Petrine authorship of 2 Peter comes with the consideration of two statements the author includes referring to "the fathers" (3:4, ESV) and Paul's letters as Scripture (3:16).
The problem with "the fathers" is that since the days of Peter, "the fathers" has come to refer to the leaders of the Church in the early time, and therefore it is argued that the author must be an imitator writing when this expression had received wide use. However, "the fathers" elsewhere refers to the Jewish patriarchs, and could easily do so here as well.
When the author mentions the letters of Paul, he gives several statements which indicate to some that he is writing from a later time period. The first such indication comes from the author's words "all his letters..." (3:16). The "all" is taken to indicate a collection of Pauline writings, which to our best knowledge did not occur until the middle (or possibly early) 2nd Century. However, Peter would have had only to know of three letters of Paul to use the expression "all" - this does not indicate a collection at all.
The second indication from the reference to Paul's writings is the author's classification of these as Scripture (3:16). Again, it is widely believed that this did not occur officially until the mid-second century, thus placing the author well beyond the limits of Peter's life. However, the author does not necessarily regard Paul's writings as accepted Scripture. Is it not possible, even likely that a fellow-apostle would be one of the first to recognise the work of God in a text? Isn't it possible that Peter considered Paul's writings to be Scripture and so mentioned them as such, even if they weren't generally regarded as such?
Finally it seems that the question of motive must be considered. If this epistle is the work of an imitator, there appears to be a lack of reason for the subterfuge. In general, psuedepigraphical letters (letters written by an imitator), are written as such in order to add orthodox weight to heretical teaching. However, the teaching in 2 Peter is quite orthodox; the author didn't need to borrow someone else's name to gain authority.
It seems that we are left with the well established attitude that we should not disregard historical attestation unless there is significant reason to do so. In the case of 2 Peter there are certainly reasons to question the authenticity (in fact 2 Peter was the most doubted of all the New Testament texts during the formation of the the canon) yet it seems that those reasons can be explained, and are not adequately significant to ignore the fact that the Apostle Peter is the only person suggested as author of this epistle.
If Peter was the author (as the above discussion tentatively indicates), the letter must have been written by 68 AD (as Peter died at c.68 AD the latest), but probably in the 60s at some point. Those who don't ascribe the letter to the Apostle Peter usually date it between c.125-150 AD.