Moshe Halbertal, People of the Book: Canon, Meaning, and Authority (Cambridge: Harvard University Press, 1997) 150.
Another debate concerning the book of Esther is mentioned in Babylonian Talmud, Megillah 7a.
I read the debate about the Book of Esther's inspiration in B.T. Megillah 7a, or, more accurately, the (Soncino?) English translation of it and the notes in my Judaic Classics Library. I can't say I understand all of it, but I'll try to relay what I learned.
We start with a story: Esther asks for her experiences to be written for posterity, and the wise men of the Jews express the reservation that this will incite the ill will of the nations, presumably because it celebrates the downfall of Gentiles. Esther responds that her story is already in the chronicles of the kings of Media and Persia, so why can't the Jews write it down for their own benefit?
Another version of the story: Esther asks the wise men of her people to write her story for posterity. The wise men refuse, replying, "Have I not written for thee three times,— three times and not four?" According to the note, the wise men are referring to Proverbs 22:20, which they understand as "Did I not write for you three things?" The note states that, in the eyes of the wise men, this passage somehow means that the Bible only discusses God's defeat of the Amalekites three times: Exodus 17:8-16; Deuteronomy 25:17-19; and I Samuel 15. That would preclude the Bible referring to it a fourth time, by including a book about Esther's defeat of the Amalekite Haman.
But the wise men backtrack, on account of their rereading of Exodus 17:14: "Write this as a reminder in a book and recite it in the hearing of Joshua: I will utterly blot out the remembrance of Amalek from under heaven" (NRSV). For the wise men in the story, "Write this" refers to the God's statement about Israel's commission to wipe out the Amalekites in Exodus 17:8-16 and Deuteronomy 25:17-19, which count as one, presumably because they're both in the Pentateuch. "As a reminder" points to I Samuel 15, where Saul carries out God's mission to destroy the Amalekites (or he does so incompletely). And "in a book" refers to the Book of Esther, where the Jews defeat the Amalekite Haman. So God's defeat of the Amalekites is mentioned three times in Scripture, as Proverbs 22:20 affirms, and Esther is one of those times. Therefore, the wise men deemed it appropriate to write a Scriptural book about Esther, filling in that third slot.
But there are rabbis who disagree, holding that Exodus 7:8-16 and Deuteronomy 25:17-19 count as two times, not one. In this view, I Samuel 15 is the third time, so there cannot be a fourth reference to God's defeat of the Amalekites in Scripture. Therefore, Esther is not inspired, according to these particular Tannaitic rabbis.
Then there's a discussion about whether or not the scroll of Esther makes the hands unclean, which means "is Scripture." Rabbi Samuel says it does not, but that Esther was still written under the inspiration of the Holy Spirit, presumably making it inspired but not canonical. Rabbi Samuel states that Esther was supposed to be recited by heart, not written down. The discussion concludes with a reference to rabbis who supported the canonicity of Esther.
Then, there is pro and con about four arguments for the inspiration of Esther, and finally a fifth argument that the Talmudic passage presents as irrefutable, meaning Esther's canonicity wins out in the end. Here are the five arguments:
1. Rabbi Eleazar refers to Esther 6:6 as evidence for the Book of Esther's inspiration: "Haman said to himself, 'Whom would the king wish to honor more than me?'" According to the note, the rationale here is that the author had no way of knowing what Haman thought to himself, except through divine inspiration. Against Eleazar's argument, Raba retorts that it didn't take divine inspiration for the author of Esther to conclude that Haman thought this. It was a logical conclusion! Haman was the highest in the esteem of the king, which was evident in his position, plus he proposed lavish treatment for the man the king desired to honor. So of course Haman thought that he'd be the one to receive the king's special treatment!
2. Rabbi Akiba said, "Esther was composed under the inspiration of the holy spirit, as it says, And Esther obtained favour in the eyes of all that looked upon her" (Esther 2:15). The note says to see the previous note, the one explaining Rabbi Eleazar's argument (see 1), so there may be the same rationale here: How would the author of Esther have known that Esther obtained favor in the eyes of all who looked on her, if he were not divinely-inspired? After all, apart from divine inspiration, one cannot know what others are thinking!
Raba retorts: "Against the proof of R. Akiba it may be objected that perhaps the fact is as stated by R. Eleazar, who said that these words show that to every man she appeared to belong to his own nation." According to Emmanuel Levinas (In the Time of the Nations 28), Eleazar means that the people of Persia assumed that Esther was one of them, not a Jew, and that's why she found favor with them. The author of Esther didn't need divine inspiration to figure that out, considering the xenophobia of Esther's time and place!
3. For the third argument, "R. Meir says: Esther was composed under the inspiration of the holy spirit, as it says, And the thing became known to Mordecai" (Esther 2:22). The note says the rationale is that Mordecai could only have learned about the plot against the king through the inspiration of the Holy Spirit. But Raba responds, "Against R. Meir it may be objected that perhaps the fact is as stated by R. Hiyya b. Abba who said that Bigthan and Teresh were two men from Tarsis." Raba may be referring to the tradition in B.T. Megillah 13a, which says that Mordecai understood Tarsisian because he knew seventy languages. The point is that Mordecai could have learned about the plot of the two men without divine inspiration.
4. In the fourth argument, "R. Jose b. Durmaskith said: Esther was composed under the inspiration of the holy spirit, as it says, But on the spoil they laid not their hands" (Esther 9:10). And Raba retorts: "Against the proof of R. Jose b. Durmaskith it may be objected that perhaps they sent messengers." What Levinas says is going on here is this: Rabbi Jose says that Esther presents the Jews as especially virtuous because they did not take spoil from their enemies, in this case, Haman's sons. Where could we find such virtue but in a divinely-inspired writing, Jose's argument runs. But Raba retorts that the Jews were on their best behavior because the Gentiles had sent their secret police ("messengers") to monitor them, and the Jews didn't want to make a bad impression. They valued their safety. That's understandable, but not exactly virtuous.
5. Now for the fifth argument: "Said Samuel: Had I been there, I would have given a proof superior to all, namely, that it says, They confirmed and took upon them, [which means] they confirmed above what they took upon themselves below" (see Esther 9:27). The verse says that the Jews promised to continue to observe Purim throughout their generations. Raba thinks this is an indication of the book's inspiration, as do other rabbis. The reason Samuel's argument is so convincing to them is that, well, the Jews continue to observe Purim. The Book of Esther said they would do so throughout their generations, and, sure enough, they do. How could the author of the book have had that knowledge, apart from divine inspiration?
From a modern perspective, these arguments look pretty bad. Can we say that a book is inspired because some of its characters appear to have divine inspiration or act virtuously? Even books outside of Jewish and Christian canons have that! There are TV shows in which that is the case! Are they divinely-inspired?
Yet, on some level, I can appreciate the questions with which the rabbis are wrestling. Are we a part of the divine drama of the Bible? Is such-and-such an event evidence of divine involvement, or can it have a naturalistic explanation? (And, to add my own question, can God work through natural means?) When we do good, is that an indication of our virtue, or rather that we're trying to make a good impression to protect or advance ourselves? And can the continued power of a text or ritual serve as evidence that God is behind it?