The science of biology and therefore how animals are classified was not developed until about the rise of Greek philosophy. Therefore to nitpick the fact bats (the only mammal that flies) was considered a bird by ancients is ludicrous. The same applies to the science of mathermatics. A circle is a circle regardless of how it is defined.
The absence of the name of Belshazzar on the monuments was long regarded as an argument against the genuineness of the Book of Daniel. In 1854 Sir Henry Rawlinson found an inscription of Nabonidus which referred to his eldest son. Quite recently, however, the side of a ravine undermined by heavy rains fell at Hillah, a suburb of Babylon. A number of huge, coarse earthenware vases were laid bare. These were filled with tablets, the receipts and contracts of a firm of Babylonian bankers, which showed that Belshazzar had a household, with secretaries and stewards. One was dated in the third year of the king Marduk-sar-uzur. As Marduk-sar-uzar was another name for Baal, this Marduk-sar-uzur was found to be the Belshazzar of Scripture. In one of these contract tablets, dated in the July after the defeat of the army of Nabonidus, we find him paying tithes for his sister to the temple of the sun-god at Sippara.
http://www.christiananswers.net/diction ... azzar.html
Matthew's genealogy refers to generations, not number of kings. Of the last 4 kings of Judah 3 were Josiah's sons and therefore of the same generation.
Now, the accuracy of the Bible, which is not a science text book has been affirmed by scholars for centuries based on the age of the available manuscripts.