Eusebius in his Historia Ecclesiastica 3.39.15 writes about Papias claiming Mark, an attendant of Peter, had written an account about Jesus:
And the elder would say this: Mark, who had become the interpreter of Peter, wrote accurately, yet not in order, as many things as he remembered of the things either said or done by the Lord. For he neither heard the Lord nor followed him, but later, as I said, Peter, who would make the teachings to the needs, but not making them as an ordering together of the lordly oracles, so that Mark did not sin having thus written certain things as he remembered them. For he made one provision, to leave out nothing of the things that he heard or falsify anything in them.
Και τουθ ο πρεσβυτερος ελεγεν· Μαρκος μεν ερμηνευτης Πετρου γενομενος, οσα εμνημονευσεν ακριβως εγραψεν, ου μεντοι ταξει, τα υπο του κυριου η λεχθεντα η πραχθεντα. ουτε γαρ ηκουσεν του κυριου ουτε παρηκολουθησεν αυτω, υστερον δε, ως εφην, Πετρω, ος προς τας χρειας εποιειτο τας διδασκαλιας, αλλ ουχ ωσπερ συνταξιν των κυριακων ποιουμενος λογιων, ωστε ουδεν ημαρτεν Μαρκος ουτως ενια γραψας ως απεμνημοσευσεν. ενος γαρ εποιησατο προνοιαν, του μηδεν ων ηκουσεν παραλιπειν η ψευσασθαι τι εν αυτοις.
Could the phrase ου μεντοι ταξει refer to the concept of a rhetorical arrangement that is not in order, in that it skips over major sections of the life and ministry of Jesus?
There are two references in the New Testament that are different, yet similar:
Inasmuch as many have undertaken to compile an account of the things accomplished among us, just as those who from the beginning were eyewitnesses and servants of the word have handed them down to us, it seemed fitting for me as well, having investigated everything carefully from the beginning, to write it out for you in orderly sequence [καθεξῆς], most excellent Theophilus; so that you might know the exact truth about the things you have been taught. (Luke 1.1-4)
But Peter began speaking and proceeded to explain to them in orderly sequence [καθεξῆς], saying.... (Acts 11.4)
The early second century literary critic Lucian in his book, How to Write History uses ταξει in a broad sense when he writes:
As to the facts themselves, [the historian] should not assemble them at random, but only after much laborious and painstaking investigation. He should for preference be an eyewitness, but, if not, listen to those who tell the more impartial story, those whom one would suppose least likely to subtract from the facts or add to them out of favor or malice. When this happens let him show shrewdness and skill in putting together the more credible story. When he has collected all or most of the facts, let him first make them into a series of notes, a body of material as yet with no beauty or continuity. Then, after arranging them into order [τάξιν], let him give it beauty and enhance it with the charms of expression, figure, and rhythm. (47-48)
Of course, it is possible that Papias is making reference to an early version of Mark's Gospel. If so, it might be similar to how Tertullian in his work Against Marcion writes:
Nothing I have previously written against Marcion is any longer my concern. I am embarking upon a new work to replace an old one. My first edition [primum opusculum], too hurriedly produced, I afterwards withdrew, substituting a fuller [pleniore] treatment. This also, before enough copies [exemplariis] had been made, was stolen from me by a person, at that time a Christian but afterwards an apostate, who chanced to have copied out some extracts very incorrectly [mendosissime], and shewed them to a group of people. Hence the need for correction [emendationis necessitas facta est]. The opportunity provided by this revision has moved me to make some additions. Thus this written work, a third succeeding a second, and instead of third from now on the first, needs to begin by reporting the demise of the work it supersedes, so that no one may be perplexed if in one place or another he comes across varying forms of it [varietas eius]. (1.1.1-2)
The target audience of Mark's Gospel appears to be Cæsar's equites. So, an abridged version of the life and ministry of Jesus might have deliberately been crafted to leave out certain events for rhetorical purposes such as memory retention, etc. For example, in the Fragments attributed to Clement of Alexandria it states (emphasis added):
Mark, the follower of Peter, while Peter publicly preached the Gospel at Rome before some of Cæsar's equites, and adduced many testimonies to Christ, in order that thereby they might be able to commit to memory what was spoken, of what was spoken by Peter, wrote entirely what is called the Gospel according to Mark. As Luke also may be recognised by the style, both to have composed the Acts of the Apostles, and to have translated Paul's Epistle to the Hebrews.
So, what is a survey of the various views that Christians related to the question of what did Papias mean when he wrote how Mark did not write "in order" about what Jesus said or did?