What astronomical events have helped determine the accuracy of historical dates of Middle Eastern (specifically Persian) events? Some examples of Middle Eastern/Persian events could be the year a king was reigning or the start/end of war. Some examples of astronomical events could be observed supernovae or comets.
All our system of exact dating of events of ancient history is based on Babylonian astronomical observations.
There is a large number of astronomical cuneiform tables found in Mesopotamia. Only in British Museum there are 20,000 of them. They are dated and contain various astronomical data (positions of the Moon, planets, eclipses etc.) which can be verified. Many of them have been published in the book: Astronomical cuneiform texts; Babylonian ephemerides of the Seleucid period for the motion of the sun, the moon, and the planets. Three volumes.1955 by O. Neugebauer.
Astronomical observation records from Babylon cover almost continuously the period since Nabonassar (747-734 b.c.). So dating the observations is possible since this time. This was done already by Ptolemy who passed to us the so-called "Canon of Kings" which is the list of Babylonian rulers since Nabonassar to his days, with dates. Cuneiform texts deciphered only in 19th century confirm this list, and it is actually the foundation for exact dating of events of the ancient history. Once the correspondence of any calendar with Babylonian one is established, we have the exact dating, accurate to one day.