What is the Biblical basis for disbelief in the doctrine of Biblical inerrancy?

Not all Christians hold to the view of Biblical inerrancy. For example, whenever there are alleged inconsistencies or alleged scientific errors in the Bible, they consider that the verses in question don't give the exact events. How are those views justified in the Bible? What verses do opponents of Biblical inerrancy cite to support their views and contradict the idea that the Bible is inerrant?