The book of Ezra talks about the return of Israel to its homeland after being exiled to Babylon, and the subsequent rebuilding of the temple in Jerusalem. Closely related to the book of Ezra is the book of Nehemiah, who came about 13 years after Ezra and led in the rebuilding of the Jerusalem city walls. The time of writing of this little book of Ezra covers the time of Ezra’s return to Jerusalem bout 458 B.C.E. and is traditionally thought to have been completed around 400 B.C.E at the latest, with only a small amount of editing after Ezra’s work. But some modern critics want to call it a late forgery, not completed until around the time of Christ, and rather than Ezra being its main author, they theorize that many editors were involved. In other words, they say it is from a later time period than it claims to be, and so Ezra couldn’t have been author of much of the book, nor would it be historically reliable.
Why do we care? Because it’s just one more attack on the historical accuracy and integrity of the bible writers, and so needs to be investigated and responded to. These objections have implications for the canonicity of the book of Ezra as well. As we shall see as we look through them, the critic’s conclusions are not so certain as they claim.
1.Claim:The critics’s claim that while the book appeared in its earliest form around 400 B.C.E., it was revised and edited for several centuries afterward. and wasn’t settled until the time of Christ. There are others who think that Ezra returned to Jerusalem much later than the traditional 458 B.C., because of a mention of Ezra staying with a certain man named Johanan son of Eliashib. (Ezra 10:6). A Johanan is mentioned as the “son” of Eliashib (Nehemiah 12:22), Eliashib being a contemporary of Nehemiah (Nehemiah 3:1) in about the 440’s B.C., but there is also a grandson of Eliashib mentioned in the Elephantine Papyrii that was later than both Ezra and Nehemiah’s time. Also, a Jaddua the high priest mentioned by Josephus as living at the time of Alexander the Great in 330 B.C.E. is also mentioned in Nehemiah 12:11, and so they say either the books of Ezra and Nehemiah must have been composed long after the actual time they lived, or Nehemiah as well as his contemporary Ezra must have lived much later than previously thought.
Response: There is a Johanan mentioned as the grandson of Eliashib in the Elephantine Papyrii, and who lived somewhat later than Nehemiah. But some scholars such as E. J. Young, think that this was not the same individual as the Johanan in Ezra who was said to be a son of Eliashib, (sometimes the term ben can refer to a grandson as well as a son). I think he probably was actually Eliashib’s grandson, as in Nehemiah 12:10-11, 22 (Johanan and Jonathan are likely the same person), and could have known Ezra when he was younger, years before his time as high priest. 
As far as the more problematic Jaddua, who was Johanan’s son, Jehoida’s grandson, and Eliashib’ great-grandson, (see Nehemiah 12:10-11) he could have known Nehemiah in his youth (Josephus wrote that Nehemiah lived to a great age), and then Jaddua lived to an old age as high priest at the time of Alexander. Let’s say Eliashib, Nehemiah’s contemporary, was around fifty when Johanan his grandson was born, and 10 years later was sixty by 446 B.C.E when he was helping Nehemiah to rebuild the wall of Jerusalem. If Johanan his grandson was therefore 20 years old in 456 B.C.E, Johanan would have been 68 by the time the Elephantine Papyrii #30 that mentions him was written in 408 B.C. So Jaddua the son of Johanan would have been born probably no later than about 420 to 410 B.C.E. and he could therefore have been a high priest of about 80-90 years old at 330 B.C. E., the time of Alexander. 
Also, Josephus may have gotten his history wrong, since he places the archaeologically verified 5th century Sanballat the governor as also being a contemporary of Jaddua. Or yet another solution is that there were more than one Jaddua and Sanballat, as even an Aramaic papyrus dating from 375-335 B.C. E. indicates 3 different Sanballats, including one contemporary with Nehemiah and another with Alexander the Great. 
2. Claim: There are also seven decrees of Persian kings contained in Ezra, and some modern scholars reject them as forgeries. They claim that the king’s titles such as “Darius the Persian” wouldn’t have been in use until after the Persian period and into the following Greek period.
Response: Recent research has shown that the title “King of Persia” was in fact used by multiple authors in multiple documents during the Persian period, with reference to at least six Persian kings, some of these even authored by the kings themselves. So this objection has no weight.
Claim: It is also claimed that the Aramaic portions of Ezra reflect a later linguistic style than fifth century Aramaic.
Response: The actual Aramaic in Ezra matches up closely with the 5th century Elephantine Papyrii, with the only differences being in places where the spelling has been modernized as the text was transmitted.  
Claim: Finally, it is claimed that the Persian king’s history in Ezra 4 is inaccurate, because it seems to go in the wrong sequence, from Cyrus (558-529) to Xerxes (485-464), to Artaxerxes I (464-424) and then to Darius I (522-485). They charge that only a late document could be so confused so the author got the order of these kings wrong.
Response: Upon examining the passage in question, Ezra 4:5-24, more closely, the author was certainly aware that the sequence of kings went from Cyrus to Darius I to Xerxes (Ahasuaerus) (see Ezra 4:5-6) And verses 6-23 seems to be a parenthetical section, in topical rather than chronological order, that looks ahead to later kings and deals with the rebuilding of the city walls rather than the temple. Then in verse 24, it brings us back to the point left off in verse 5, where the temple had not yet been rebuilt. Notice in the topical section 4:6-11 does not refer to the temple but city walls only since the temple had already been rebuilt.  The biblical writers often departed from time order and grouped things rather by topic, so this is not a proven error at all.
As we have seen, there is no reason to believe that this book of Ezra, an important book in the history of Israel, is anything but totally authentic historically.
 Archer, Gleason, A Survey of Old Testament Introduction, Moody Press, Chicago, 1994, pp. 459-460.