The next contradiction is a small conundrum from the Gospel attributed to John. Full context here. All Bible verses are taken, of course, from the one and only perfectly preserved English translation of the Bible.
After these things came Jesus and his disciples into the land of Judaea; and there he tarried with them, and baptized. And John also was baptizing in Aenon near to Salim, because there was much water there: and they came, and were baptized.
When therefore the Lord knew how the Pharisees had heard that Jesus made and baptized more disciples than John, (Though Jesus himself baptized not, but his disciples,) He left Judaea, and departed again into Galilee.
Prior to reading chapter 4, a straightforward reading of 3:22 would lead most people to conclude that Jesus had both tarried and baptized with his disciples. When we get to 4:2, however, we find that Jesus should not be considered to have been personally engaged in acts of baptism. There are several possible hermeneutical workarounds for this problem.
One solution, suggested by Jerome Murphy-O'Connor (Professor of New Testament at the École Biblique in Jerusalem) is that these two verses were authored by two different people, the later of whom was attempting to put a midrashic gloss upon the earlier account. In an article published in New Testament Studies he posits the possibility of "a Johannine editor, whose specific contribution is to be found in the interpolation at John 4:2." This does not eliminate the contradiction inherent in a plain reading of these two passages, but it does explain how such contradictory passages could end up effectively side by side, evidently situated within the same gospel pericope.
Another solution has been suggested by Calvinist blogger Alan Maricle who claims that Jesus "didn't physically immerse people with His own hands" but rather deputized his disciples to do the baptizing for him. To accept this view, one must take John 3:22 to mean "he tarried with them and [they] baptized" while Jesus merely supervised. The problem with such an attempted reinterpretation is that the verb form of baptise doesn't allow for it. Here, βαπτίζω is used in the imperfect active indicative third person singular form. To quote Dr. Peter Moses, "In this verse we have the imperfect active indicative of baptizo in the third person singular. The imperfect tense shows continual action whilst the third person singular indicates that at this stage Jesus Himself kept on baptizing people."
There are other solutions, to be sure, such as the hypothesis that these two verses represent two distinct phases in Jesus' ministry. According to this model, Jesus personally baptized some of his early followers, and later deputized his inner circle to do the baptizing on his behalf or in his name. It borders on special pleading, however, to attempt to read this transformation of Jesus' ministry into a single pericope spanning John 3:22 through 4:3, describing a single missionary trip from Galilee into Judea.
Of all the possible solutions, I personally find Murphy-O'Connor's hypothesis most plausible, because it explains both the parathetical and paradoxical nature of 4:2, which reads on its face like an editor's note correcting an error in the original text. Of course, such a solution is not available to those who consider 4:2 to be inherent to an innerrant autograph, but it must be noted that (alas!) we simply do not have the original manuscripts.