There is SOME rabbinic thinking in the New Testament such as binding and loosing, as D.A Carson notes:
"“Formally ho is neuter, and ‘things’ might be expected. Moreover, the rabbis spoke of ‘binding’ and ‘loosing’ in terms of laying down Halakah (rules of conduct): Shammai is strict and ‘binds’ many things on people, while Hillel allows greater laxity and ‘looses’ them. It might be argued, then, that in Acts 15:10 Peter looses what certain Judaizers want to bind. Yet despite this, it is better to take binding and loosing in Matthew 16:19 to refer to persons, not rules. The neuterhosa (‘whatever’) occurs in 18:18 where the context demands that persons are meant. Indeed Greek often uses the neuter of people for classes or categories rather than for individuals. The context of v. 19 supports this; for the keys in the preceding context clause speak of permission for entering the kingdom or being excluded from it, not rules of conduct under heaven’s rule”" (12.) D.A. Carson, Matthew, ed. Frank E. Gaebelein, The Expositor’s Bible Commentary, Vol. 8, [Grand Rapids: Zondervan Publishing House, 1984], p. 372).
We do have an example of a rabbinic concept that is found within the context of the NT. My thanks to Keith Thompson for using this in his article on Peter being the rock which can be found here: http://www.reformedapologeticsministries.com/2013/02/my-thesis-on-matthew-16-was-peter-pope.html (This link is now defunct).
However, there are cases where the Jew, through their rabbinic lense, assumes that the Judaism of Jesus' day was similar to the Rabbis of later centuries.
One person who I spoke with mentioned Acts 8:32, Unfortunately there was a little mockery behind it considering he laughed at the idea of the apostle revealing who Isaiah 53 was talking about to the eunuch who inquired about it.
This is strange because counter missionaries, rather than your average Jewish person (average is not intended as an insult) often assert that the apostles NEVER read Isaiah 53 as Messianic because the apostles themselves did not expect Jesus to suffer and die, this anathema to their thinking at that point. This is often used as a means to try and say that Isaiah 53 being Messianic is made up by Christians, in point of fact that you do have Rabbinic Writings, including the paraphrases known as the Targums, which actually do identify it as a prophecy of the Messiah, though the interpretation is not the same as the Christian interpretation. I briefly allude to this and quote the Rabbinic sources in this article response to Shadid Lewis which can be found here: http://answering-judaism.blogspot.co.uk/2013/10/response-to-shadid-lewis-on-isaiah-53.html
Yes I am aware of Origen speaking about Jews saying it's about a group in Contra Celsum, but how this would prove the Messianic interpretation false I don't know, although this does discredit the idea and refute the notion that Rashi was the first Rabbi to say it is about Israel, which is a common misconception held by a majority of people. To point of fact that the eunuch who came Philip to give an example from the NT, was actually asking people about the suffering servant and DID NOT know who it was, and I need to remind the audience that the eunuch was convert to Judaism.
Nakdimon makes an interesting observation regarding Origen (https://sites.google.com/site/nakdimonspage/isaiah-53-part-2), he says:
"Origen: Now this is the only pre-Rashi source that I have been confronted with in my years of debating anti-missionaries that gives us a literal reading of Israel being the servant in Isaiah 53. Note that it’s not even a rabbinic source! That’s how rare this view was. But let’s see what Origen is saying exactly in chapter 55 of his book:
There is an assumption on the part of some of the Rabbinic Jews that they were in uniform agreement that Isaiah 53 is not Messianic, forgive me if I have misrepresented the position of the Rabbinic communities. Does one honestly think that the Jews would of had ONE uniform view of the Messiah in Jesus day? The only uniform view would of been was his ushering in of universal peace, ingathering of the Jewish people and the fact he had to come from the Davidic line.
Now I believe in the inspiration of the New Testament, But for arguments sake, we'll put that aside for now in this article and focus on it being a historical document. It records some of the opinions of the people of that time and how certain passages were deemed Messianic, such as Micah 5:2, Zechariah 9:9 and Daniel 7:13-13.
The Talmud centuries later postulates a possible interpretation of Zechariah 9:9 and Daniel 7:13-14:
"R. Alexandri said: R. Joshua b. Levi pointed out a contradiction. it is written, in its time [will the Messiah come], whilst it is also written, I [the Lord] will hasten it!33 — if they are worthy, I will hasten it: if not, [he will come] at the due time. R. Alexandri said: R. Joshua opposed two verses: it is written, And behold, one like the son of man came with the clouds of heaven34 whilst [elsewhere] it is written, [behold, thy king cometh unto thee … ] lowly, and riding upon an ass!35 — if they are meritorious, [he will come] with the clouds of heaven;36 if not, lowly and riding upon an ass. King Shapur [I] said to Samuel, 'Ye maintain that the Messiah will come upon an ass: I will rather send him a white horse of mine.'37 He replied, 'Have you a hundred-hued steed?'" (Sanhedrin 98b http://www.come-and-hear.com/sanhedrin/sanhedrin_98.html)
Now of course I am not saying the Talmud is my authority on this matter, I am just simply making a point that Zechariah 9:9 and Daniel 7:13-14 being Messianic not only according to Christians, but even some of the Rabbis did too, with obvious differences, considering the Talmudic tradition above speaks of one coming happening or the other depending on how the Jews respond to God. If righteous, the Messiah comes on the clouds of heaven, or if they are wicked, he'll come riding on a donkey, Whereas Christians say the Messiah first came on a donkey and in his second coming will come on the clouds of heaven, which Jesus alludes to numerous times.
Anyway, The point here is that the NT records what some of the Jews in those days had believed, though some of their conclusions where wrong, such as the Messiah coming from Galilee. Jesus was raised in Galilee but born in Bethlehem and raised in Nazareth.
Supposed Oral Tradition
A common assertion made by many, including Contra Brown author Yisroel Blumenthal, and the late Dr Immanuel Schochet, is that Jesus told the apostles to listen to the Rabbinic traditions given by the Pharisees, Often misusing Matthew 23 to justify the idea of an oral Torah in the time of Moses:
"23 Then Jesus said to the crowds and to his disciples: 2 “The teachers of the law and the Pharisees sit in Moses’ seat. 3 So you must be careful to do everything they tell you. But do not do what they do, for they do not practice what they preach. 4 They tie up heavy, cumbersome loads and put them on other people’s shoulders, but they themselves are not willing to lift a finger to move them.
5 “Everything they do is done for people to see: They make their phylacteries[a] wide and the tassels on their garments long; 6 they love the place of honor at banquets and the most important seats in the synagogues; 7 they love to be greeted with respect in the marketplaces and to be called ‘Rabbi’ by others."
I have already stated the following in my first article response to "Supplement to Contra Brown" regarding this issue:
"Jesus is anathematizing the Pharisees for their wickedness and hypocrisy. He tells the disciples to obey them but not emulate them. In other words it's to do with the Torah, not the rulings of the Pharisees, although the tradition consistent with the scripture wouldn't of been harmful. He is not saying that we are to accept the Oral Torah because there isn't one, this is Rabbinic Jewish anachronicism being read into the New Testament. The NT may be Jewish, but not necessarily Talmudic."
Simply put, an exhortation from Jesus to pay attention to the Pharisees and submit to them, would not prove a binding oral law was present in that time.
It is possible for many to be subject to reading both the TANAKH and the NT with coloured glasses, That is something that one can end up doing if we are not careful, Hope this article has been of help.
Note: This article if the Lord Wills may be expanded upon.