Examines the issue over whether or not Jesus kept the torah perfectly.
You may wish to begin with Did Jesus Lie which discusses a fundamental issue with one instance of Jesus' ministry as portrayed in the Gospels.
One aspect in how Jesus would have had to fulfill the Jewish law is in the sense where he would have had to fulfil every Messianic prophecy – in order to be – the Messiah. Yet we see that there are several cases where there are unfufilled Messianic prophecies.
Also, if Jesus made some statement which contradicted himself, or the Old Testament, or any other facet of Christian Doctrine, such as issuing a prophecy that never came true or accidentally overstepping the bounds of the Torah (or not fulfilling the Torah) then we would say that he lied in the sense that if we say he claimed to be the Messiah (or even only that he laid claim to it by his actions, rightfully or not, intended or not) – then he would have impeached himself from making such a claim.
A common defense I have heard (to some of what I am about to present) is that since Jesus would be presumed to be God, then he would have the authorization to make a change to God's word. This is not a logical claim. First, we reject it because it is a highly visible failure of the test of who is and is not from God – a test which God gave us specifically to test the viability of any such prophet or Messiah. Secondly, because of why it would fail the test – as we take the axiom that God is perfect, would not lie to us about his plan, and that he can predict the future (he created time and exists outside of it's bounds). It is not logical to assume he would make one statement and then later contradict himself in such a manner. Therefore we can only conclude that Jesus is not God in such a case, which would then amount to a lie (since Jesus claimed or laid claim to it).