Why does Mark mention Elijah before Moses?
The order switch indicates that Matthew and Luke were more adept at handling the symbolism of the historical event than Peter and Mark were. There are two reasons for this: Peter was the least educated of the three (Matthew, Luke, Peter) and he also wrote earlier than the other two, so they had more time to develop a more detailed understanding of the events in the context of prophecy.
In a purely literal interpretation, the order of naming the people at an event has little significance. But when considering the prophetic nature of the event, the order is significant.
This should not be unfamiliar to us, since even in secular events, when consideration is given to custom, deference is given in listings to those of higher stature.
In this case stature is not the deciding factor, but a preference for the prophetic order of 'Word, Works, Life' as a motif.
This order can be observed many places in the scriptures. One such example, is that of the three women at the well. Rachel was chosen (Word), Rebeckah was wooed and worked for (Works), and the people of Sychar were gathered (Life). The motif is used to highlight the primary participation in obtaining a bride for 'the man' Christ Jesus. The Father chooses, the Son works for, and the Holy Spirit gathers the bride.
The example of the order being changed by Matthew and Luke indicates that they saw the motif where Peter didn't. This gives us insight into the mechanism of the inspiration of the scriptures. The authors didn't just have instantaneous knowledge. But as they studied, and as the Holy Spirit brought things to remembrance, they were able to correlate the scriptures (OT) with what they knew about Jesus. They wrote down things that indicated that Jesus fulfilled scripture.
John, who wrote last and had the greatest insight into prophecy, demonstrates the most developed use of the OT motifs and prophecies as he tells us that Jesus fulfilled scripture. His adept handling of prophecy begins with John 1:1-4 where he exposes the most sublime teachings contained in Gen 1:1 from the Hebrew text itself. Those who are unable to reproduce John's hermeneutic are relegated to supposing that John obtained his ideas of the Logos from Greek philosophers.
Back to the OP: Moses represents the Word since it was he who was the mediator of the Word. Elijah represents the mighty Works of God, having stopped the rain for three years and called fire from heaven. Christ represents the Life for obvious reasons.
Peter understood the parallel between Jesus's baptism and the transfiguration sufficiently to relate the event, but insufficiently to relate the more subtle particulars.
John wrote to a Greek audience to answer the question "Why should we accept Jesus as a God-Man when we have been burned so many times by Man-gods?
Since the transfiguration was only witnessed by three people, it would carry relatively little weight in his argument. Instead, he relies upon the Greek familiarization of what Clement called plagiarization of Hebrew wisdom by Greek philosophers. They were familiar with the Hebrew 'origin myths' as many even today call them. But he used Gen 1 as a fact of general revelation; something that all men were familiar with, and built a picture of a God who was humble (even accepting rejection by his own), rather than a man who claimed divinity.
John boldly declares that the son (bar) is the word which created (bara) which was in the beginning (bara-shit) and that he was with God (bara Elohim) and also being the Life (l'heim) the Light (a lo khoom) and later even the bread (lechem), by using methods of interpretation which are still used by rabbis today, and which unpack the mysteries made known in Christ.
With the testimony of the mystery of the ages at his fingertips, it was unnecessary for him to even mention the fairly private event of the transfiguration.
The word order in Mark does have meaning. It is placing the emphasis on Elijah rather than upon Jesus's birth. Mark starts with the preaching of John fulfilling the prophecy that Elijah would come first. His order points back to that.
