No, Scripture does NOT say Jesus said many things not written down, only that Jesus DID many things that HAD they been written down, it would take up ALL the resources of the world to contain them - obviously speaking of the full knowledge of God:
Jesus did many other things as well. If every one of them were written down, I suppose that even the whole world would not have room for the books that would be written. (John 21:25)
Rome has used the verse in John, however, to justify their declaring ANYTHING they can think of to being part of those "things" Jesus did and include them as part of the "tradition" to be held as valid as Holy Scripture. The Apostle John mentions in his gospel that Jesus said to them:
And you also must testify, for you have been with me from the beginning. (John 15:27)
That is why John says:
The man who saw it has given testimony, and his testimony is true. He knows that he tells the truth, and he testifies so that you also may believe. (John 19:35)
And then ends with the words about the things Jesus did and leaves us with the reason why John wrote down what he did:
This is the disciple who testifies to these things and who wrote them down. We know that his testimony is true. (John 21:24)
And, prior to this, he said - after the resurrection:
Jesus performed many other signs in the presence of his disciples, which are not recorded in this book. But these are written that you may believe that Jesus is the Messiah, the Son of God, and that by believing you may have life in his name. (John 20:30-31)
My contention is that what matters to our salvation HAS been written IN Scripture and NOTHING has been omitted that must be filled in by "theologians" centuries later. The Bible is the authority because it is GOD-breathed. Trusting in sinful, fallible men to tell us what God saw fit to record for us as well as giving each of us His Holy Spirit, who would teach us all things, is foolish. The "illiterate" fishermen Jesus called to be His Apostles sure didn't STAY that way and everything Christ revealed to them, has been preserved for us to this day. The Holy Spirit is the same.
Thanks boatbums, very informative post.