There is among them a section who distort the Book with their tongues: (As they read) you would think it is a part of the Book, but it is no part of the Book; and they say, "That is from Allah," but it is not from Allah: It is they who tell a lie against Allah, and (well) they know it! (Sura al Imran 3:78)
According to early commentators Abdullah Ibn Abbas (A.D. 619-687) and Wahb Ibn Munabbih (A.D. 655-737), this verse demonstrates that although the Jews can alter the meaning of the text by reciting in their tongues (i.e. orally) something other than what the written text actually says (or writing them, if one includes books like the Mishnah), they cannot change the actual contents of the text, which remain uncorrupted.
Several centuries later, however, Ismail Ibn Kathir (A.D. 1301–1373) states otherwise and argues that the text of the Bible (or rather, its Arabic translation) has indeed been altered. It is noteworthy to look at his commentary on the verse in question to see how he interacts with Ibn Abbas and Ibn Munabbih on this subject:
Allah states that some Jews, may Allah's curses descend on them, distort Allah's Words with their tongues, change them from their appropriate places, and alter their intended meanings. They do this to deceive the ignorant people by making it appear that their words are in the Book of Allah. They attribute their own lies to Allah, even though they know that they have lied and invented falsehood. Therefore, Allah said, (and they speak a lie against Allah while they know it.) Mujahid, Ash-Sha`bi, Al-Hasan, Qatadah and Ar-Rabi` bin Anas said that, (who distort the Book with their tongues,) means, "They alter them (Allah's Words).”Al-Bukhari reported that Ibn `Abbas said that the Ayah means they alter and add although none among Allah's creation can remove the Words of Allah from His Books, they alter and distort their apparent meanings. Wahb bin Munabbih said, "The Tawrah and the Injil remain as Allah revealed them, and no letter in them was removed. However, the people misguide others by addition and false interpretation, relying on books that they wrote themselves. Then, (they say: "This is from Allah," but it is not from Allah;) As for Allah's Books, they are still preserved and cannot be changed.'' Ibn Abi Hatim recorded this statement.However, if Wahb meant the books that are currently in the hands of the People of the Book, then we should state that there is no doubt that they altered, distorted, added to and deleted from them. For instance, the Arabic versions of these books contain tremendous error, many additions and deletions and enormous misinterpretation. Those who rendered these translations have incorrect comprehension in most, rather, all of these translations. If Wahb meant the Books of Allah that He has with Him, then indeed, these Books are preserved and were never changed.(Tafsir Ibn Kathir. Commentary on Sura 3:78. Italics mine.)
(Note: When the commentary refers to the "books that they wrote themselves," this is most likely a reference to the Mishnah, since it is in the Mishnah that Jews compiled their rabbis' interpretations of the Scriptures.)
So we see that there has been an evolution in Islamic thought regarding the authenticity of the Bible. Early Muslim scholars and commentators teach that the Qur'an testifies to the authenticity of the Biblical text, and it is only the Jews and Christians who misinterpret this text. Later on, however, it would appear that once Arabic translations of the Bible have become available to the Muslims, they began to allege that it is not just the interpretation of the Bible but the very text itself (or at the very least, the Arabic translation of the text, since most Muslims did not have access to the original Greek and Hebrew) that has been modified, as seen by the contrast between the interpretation of Sura 3:78 provided by Ibn Kathir with that provided by his predecessors Ibn Abbas and Ibn Munabbih.
At the face of it, it is quite clear that the verse teaches only that the Bible has been misinterpreted, not that its text has been corrupted, since it talks about sections of it being distorted only with their tongues (not their pens).
Furthermore, although "a party" from among Jews have been accused of tampering with the written text (Sura al Baqarah 2:75-79), this charge is never made against all Jews (in fact, the context seems to limit the charge of tampering to a small faction during the time of Moses), and it is certainly never made against Christians. After all, even the Qur'an states that not all Jews and Christians are alike, and that some of them recite the contents of the books correctly (cf. Sura al Imran 3:113-115).
This, coupled with various Qur'anic references to the confirming of the books that were "between his [i.e. Muhammad's] hands ... the Law (of Moses) and the Gospel (of Jesus)" (Sura al Imran 3:3) and injunctions to "ask those who have been reading the Book from before you" (Sura Yunus 10:94) demonstrate that the Qur'an testifies to the overall authenticity of the text of the Bible.
UPDATE (June 11, 2012):
For anyone who is interested in further probing the subject of the "tampering traditions" in Islamic commentaries on the Qur'an, Gordon Nickel recently published a book entitled Narratives of Tampering in the Earliest Commentaries of the Qur'an. It is published by Brill, so one can expect it to be quite pricey. Fortunately, there happens to be a copy available at Robarts Library in the University of Toronto, so I am able to borrow the copy there. So far, it is very good scholarship, and provides strong evidence for the fact that the accusation of textual corruption of the Bible was not part of the theology of the early Muslims, but arose later in response to debates against Jews and Christians.
UPDATE (June 11, 2012):
For anyone who is interested in further probing the subject of the "tampering traditions" in Islamic commentaries on the Qur'an, Gordon Nickel recently published a book entitled Narratives of Tampering in the Earliest Commentaries of the Qur'an. It is published by Brill, so one can expect it to be quite pricey. Fortunately, there happens to be a copy available at Robarts Library in the University of Toronto, so I am able to borrow the copy there. So far, it is very good scholarship, and provides strong evidence for the fact that the accusation of textual corruption of the Bible was not part of the theology of the early Muslims, but arose later in response to debates against Jews and Christians.