Some would call these two chapters a skeptical goldmine. Dennis McKinsey writes: "...we have a listing of the subclans that returned from the Captivity and the number of people in each. In the KJV, out of approximately thirty-five subclans listed over half of the numbers are in disagreement. Furthermore, someone doesn't know how to add very well because the totals are in error. Ezra 2:64 says `The whole congregation together was 42,360,' when one can see by easily adding the figures together that the total is 29,818. Nehemiah 7:66 also says, `The whole congregation together was 42,360' when one need only add those figures to see that it's actually 31,089. Ezra erred by 12,542, and Nehemiah erred by 11,271."
It should be immediately recognized that both the authors of Ezra and Nehemiah are aiming to convey exact figures. It would be the height of laziness and unfaithfulness to the intended meaning of the text to state that we are merely dealing with round figures. Those who read 1 Esdras will run into the same problem with the total there as well. Do we here have a bona fide case for errors in the autographa? Any reasonable apology that is faithful to the evidence and to the possibility that we might have a genuine error here must address two problems: first, the divergences in the number of people in the clans listed both in Ezra and Nehemiah; second, how to account for the far-off totals.
Let the first issue be addressed. Both Ezra and Nehemiah are referring to the same event here, the return from the Babylonian Captivity. This event is not punctiliar but is an event that was realized in an interval and not a point of time. If it is reasonable to conjecture that perhaps the lists in Ezra and Nehemiah reflect the counts at different times during the time interval in which the return took place, then we have a reasonable possibility (but of course dogmatism must be avoided!) for explaining some of the divergent numbers. Higher totals might reflect clans who added people along their journey, lower totals might reflect deaths or certain types of attrition on the journey (say). Most of the divergences are fairly small: the largest divergences are between the count for Seenah (Ezra 2:35 and Neh 7:38, Nehemiah as 300 more), Azgad (Ezra 2:12 and Neh 7:17, Nehemiah having 1,100 more), Zattu (Ezra 2:8 and Neh 7:13, Ezra having 100 more), the men of Bethel and Ai (Ezra 2:28 and Neh 7:32, Ezra having 100 more). Note that these are all round-number divergences: 100, 300, and 1100. There are also some sizable numerical divergences not expressed in round numbers: the case of Hashum (Nehemiah has 105 more), Arah (Ezra has 123 more), and Adin (Nehemiah has 201 more).
Assuming that the reasonable conjecture that Ezra and Nehemiah present counts at different times in the return for argument's sake, I am at a loss to say dogmatically that this conjecture reasonably explains the differences. I have reservations concerning believing that the conjecture reasonably explains the differences -- the difference of 1,100 for Azgad seems on the surface too large a difference to account for by stating that the lists were composed at different times. The serious student of the problem can profit by reading the discussion of this problem by Archer in his Encyclopedia of Bible Difficulties , pp. 229-231, and by consulting Keil and Delitzsch's Old Testament Commentary on Ezra 2, pages 1352-1367, (page numbers for the Associated Authors and Publishers edition).
In reading the aforementioned works which represent the conservative viewpoint, one will find that the solutions are conjectural. The reader who is genuinely interested in the problem can decide for himself or herself if the discussions of the problem strain credulity or assume too much. I am an agnostic on the problem with the information out there. But we conservatives must admit at once that the Ezra/Nehemiah discrepancy is a genuine issue whose final solution eludes us. Perhaps future research will uncover information that clarifies the issue in a way that makes harmonization seem more reasonable. Perhaps future research will clarify the issue in a way that makes the problem harder for those who would try to reconcile the discrepancy. Perhaps we have as of the present all the information that we will ever have.
As we don't have all of the information, the reader will have to decide for himself or herself whether or not dogmatism for an error in the originals is warranted. I personally have seen enough divergences reconciled in my studies, both Biblical and non-Biblical, to know that what appears as a blatant error turns out to have a nice (but not necessarily simple) solution. I have confidence here that more facts which one could obtain by "being there" would help us reconcile the numerical differences. But, honesty compels me to admit that this confidence is based on past experience more than the facts in this case.
On the other hand, the major apologists such as Archer and Geisler in their books express the possibility of their presented solutions being true with much greater confidence than I do. So, the opinion among apologists is varied. But the reader should keep in mind that this difference of opinion among apologists in no way nullifies the strength of the problem which must be faced. (JPH note: a reader has pointed out that Nehemiah declares that he found this register, which means only that he is required to have inerrantly reported its contents -- not that the contents of what he found be inerrant.)