A Catholic priest would probably claim that the new testament supersedes the old. In other words, that it is Jesus' commandments we must follow now (love God with all your heart/mind/soul; love your neighbor as yourself). We are not held to the OT law, which no one could ever fulfill, but are forgiven and justified by Jesus' sacrifice. (Pardon the crudeness of this interpretation; I think I have the gist.) This does not mean there is no internal contradiction in the NT, or that Catholic traditions and requirements adhere completely to it, Neither is the case. The focus on the NT, however, sets the bar much lower.
The Bible only appears as "harmonized" as it does because it was compiled, edited, packaged, etc. by a small group in the early church with a very definite political/bureaucratic agenda. They compiled it to suit their purposes, deliberately excluding other contemporary writings that did not, and then labelling these "heresy". Perhaps the ultimate self-fulfilling prophecy.
Finally, I see a role for reason in determining one's beliefs, but by reason I do not mean logic, or objective/historical fact. An important function of reason is to check internal consistency, to measure actions against faith, and to measure both against reality. None of this proves anything on the spiritual plane, but it provides a much firmer foundation for personal belief than "mere" tradition, or externally imposed belief.