There are actually two parts to this question:
1. How can a text which contains obvious contradictions be taken literally? This appears to create a logical dilemma which cannot be solved with a literal interpretation.
2. How can one resolve these logical contradictions while maintaining a literal interpretation?
Some examples of contradictions within the Bible include (but are not limited to):
The stories of Genesis 1 and Genesis 2. Namely, the in order in which creation occured.
Jim Meritt Bible Contradictions » Internet Infidels
The number of animals taken on the Ark by Noah in Genesis 7:2 and 7:8 / 7.9.
Jim Meritt Bible Contradictions » Internet Infidels
The last words spoken by Jesus as told by Matthew, Luke and John.
Jim Meritt Bible Contradictions » Internet Infidels
Edited by Dave B, : Added examples of Biblical contradictions.