What the Pope is saying is pretty clear and is consistent with Christian and Jewish tradition: the Scriptures of Christianity and Judaism need to be interpreted and applied by means of reason in order to be made understandable and real at any stage in human history.
In both traditions, there is the view that one of the glories of the human person is the ability to reason, to see what needs to be seen in Scripture, to find the emphasis, etc. The Jewish tradition virtually places at its center the long tradition of Rabbinic discussion on the meaning of Bible texts and the laws that were handed down orally from Moses. And the Christian tradition has always seen that all of the Bible needs to be interpreted and applied (otherwise Christians would be stoning a whole lot of people every day), that the task of interpretation is to find the SENSE of Scripture, and that many passages contain more than one Sense.
The Pope is saying, in contrast, that if you believe that the sacred text is a dictation from the mouth of God, then of course the human mind can do nothing in the way of interpretation and application into life.
Thus, Islam does not have the intellectual and theological mechanism to even consider the possibility that some of the passages of the Koran should be read metaphorically or spiritually instead of literalistically.
Technically, according to Islamic practice, the Koran cannot even be translated. The few groups (such as the Sufis) that have tried to do a metaphorical interpretation - which is what Christians and modern Jews do with the more aggressive passages in the OT - have always been condemned as heretical.
The New Testament is not a problem in Christianity, because there is nothing in it that is evil, and the few things that could provide room for obsession (women keeping their heads covered, for example) are simply cultural things related to the culture of the time. Since Christianity develops, it is not tied to forms of dress.
The OT is not a problem either to Christians or Jews, because the truths that are in it are very obvious, and the historical/cultural things (such as dashing the children of your enemies upon the stones) are also obvious, and it's easy to separate the two.
The big difference is that Islam is a false religion, and Judaism and Christianity (although they conflict on whether or not the Messiah has arrived) are not.