In principle I'm sure you'd agree that there can't be any contradiction between the Bible and Nature, ...
There is no such principle.
The Bible is written by men. They may have been inspired, but they were fallible.
, but there IS contradiction on some points between the Bible and Science (evolution really, not any other areas of science).
Wrong.
Genesis 1 quite clearly is in contradiction with physics. The flood story quite clearly is in contradiction with the observed flora and fauna of Australia.
I emphasize these two, because they were what I noticed as a teenager, before I had ever heard of evolution. Those contradictions helped me recognize that the Bible was the work of men, and that it was written for the pre-scientific people of that time. It is not a problem for the Bible that there are such contradictions, but it is a problem for the assumptions of inerrancy that some make.
We have no reason to believe that the Bible is to be read like a newspaper or a science text.
No, it is to be read straight as written. It's obviously neither a newspaper nor a science text, far from both.
Yes, I agree that it is to be read straight as written. And, straight as written, it is clear that the Adam and Eve story and the Noah's ark story are both ancient fables, rather than historical fact.