There is a very interesting responsum by R. Hayyim Hirschenson (occasionally referred to in the j-blogosphere; possibly first called attention to by R. Louis Jacobs) on the question of Bible criticism.
From chapter 7 of We Have Reason To Believe (1957):
"One of the most original thinkers among the Rabbis of the older school, Rabbi Hayyim Hirschenson, wrote some years ago a fascinating Responsum on the Jewish attitude to Bible Criticism. Hirschenson, who was asked if Bible Criticism may be taught at the Hebrew University, endeavoured to apply Halachic method to the problem. The Halachah knows of three categories with regard to liability—these are, hayyabh, 'obligation', i.e. the incurment of a penalty; patur 'exemption' but assur 'forbidden', i.e. though there is no penalty for the offence there is prohibition; and patur and muttar, 'exempt and permitted', i.e. not only is there no penalty but there is no prohibition. With regard to Sabbath law, for instance, work prohibited in the Bible involves the full penalty of Sabbath desecration; work forbidden by rabbinic law is prohibited but there is no penalty attached to the prohibition; and there are certain forms of work involving no prohibition whatsoever. Hirschenson suggests (Maiki Ba-Kodesh, Vol. I and II, St. Louis, 1919-1921) that the main objection in the Talmudic sources to the rejection of the doctrine of 'Torah from Heaven' is that such a rejection impugns the honesty of Moses by suggesting that he wrote something he had not received from God. The hayyabh offence in this field, for which the penalty of exclusion from the World to Come is incurred, is the denigration of Moses' character in maintaining that he willfully forged the Biblical documents. On the other hand, the study of textual criticism is both patur and muttar, for, as we have seen, such criticism was at times resorted to in the Talmudic age. Modern Bible Criticism does not suggest that Moses forged the documents but that they are not the work of Moses at all. This, because it is in opposition to the established traditions of our people, is assur 'forbidden', but not hayyabh. Hence, Hirschenson concludes it would not be necessary for the orthodox Jew to boycott the Hebrew University because some of its Professors espouse the cause of Higher Criticism."
To expand on these words, the responsum begins by noting that as in all areas of Jewish law, there are subtle distinctions between different acts, as in hilkhos shabbos. For example, there are those things for which a person is hayav. There is patur aval assur. There is patur and mutar. He proceeds to explain how these distinctions apply to Bible criticism.
In the first case, one is hayav (by this he means hayav kares) if they say that Moshe wrote something in the Torah which he did not receive from God. (Parenthetically, this is either naivety, since Bible criticism does not generally accept that Moshe wrote anything at all or it is merely an attempt to frame the issue in traditional parlance, since the Talmud contemplates the heresy of denying that Moshe wrote the Torah by God's instruction, but not that he wrote it himself.)
In the category of patur aval assur is higher Bible criticism, that is he says that this or that part of the Torah was taken from another place, wasn't written by Moshe, etc. While this is a very bad thing, and is prohibited he is not hayav kares, nor he has not forfeited his heleq in olam habah. But it's a very bad thing. Similarly, with lower Bible criticism, a textual critic who investigates the history of the text of the Torah who plans to establish a text which is different from the present one (contra R. Jacobs who does not note this distinction, but only the one below).
In the third, patur and mutar, he places a textual critic who has no plan to change anything, but he uses critical tools for better understanding the text, or even to study Higher Criticism for the sake of knowledge, which is a good thing since it enables one to answer the epiqoros. This is no different from the Rambam's study of Greek philosophy, which contained good things and also many things that contradict religion and need to be rejected. This would be forbidden to teach children, but grown men who are university students are capable of making distinctions and can handle this material.
Finally, a fourth category, which is both a mitzvah and obligation: to become learned in massorah and dikduk, as this is an exalted practice of our forbearers and it strengthens the Torah.
For more on R. Hirschensohn (who was an associate of Ben Yehuda), see.
This teshuva and a lot more fascinating discussion can be found toward the end of מלכי בקדש חלק ב.
Thanks to Dan for suggesting this post. (link)