Jesus Contradicting Old Testament

Technically, there aren't any contradictions between the Old and New Testaments, though some of their practices were different. The reason for the different practices can be explained by what is often referred to as the progress of redemptive history. That's a fancy way of saying that in the different practices in the New Testament are really just fulfillments of practices in the Old Testament. For example, we no longer offer animal sacrifices not because God no longer demands sacrifice, but because: 1) even in the Old Testament the animal sacrifices weren't sufficient, they pointed to something bigger beyond themselves; and 2) Christ, the true sacrifice to which the animal sacrifices pointed, has now come and offered himself as a sacrifice for sin, and his one sacrifice is sufficient to fulfill for all time God's required sacrifices.

As far as the creation story itself goes, I would say there is every reason to believe it because it is God's word. However, that does not mean that a superficial reading of it is necessarily the most accurate reflection of the meaning that Moses intended. For example, if Genesis 1 is a literal account of the creation, and if Genesis 2 is also a literal account of the creation, then potential problems arise because Genesis 2 seems to contradict Genesis 1 (things appear to be created in a different order, etc). Genesis 2:4 states that "this is the account" of the creation, and stylistically (in Hebrew) it is evident that this statement refers to the account in Genesis 2, not Genesis 1. This appears to mean that Genesis 2 is accurate history. Genesis 1 contains no claim to being an actual account. Some have argued that Genesis 1 is really a poem or a song, and that its account is highly metaphorical.

Then again, Genesis 1 may also be literal history. Exodus 20:11 and 31:17 appeal to the fact that creation took six days in order to support the practice of Sabbath. Further, it is not impossible to discover reasonable interpretations of Genesis 1-2 that treat both creation accounts as literal history and also resolve apparent contradictions. For an example of this approach, you might find of interest Because it Had Rained, part 1 and Because it Had Rained, part 2 by Dr. Mark Futato.