I'm a bit skeptical as all of the events used for dating are quite common. The constellations would appear every spring. The new moon occurs every 28 days. The particular alignment of the two planets would probably occur at least once a year, maybe more than once. Having said that, I have not done the math and it is possible that the exact confluence of these otherwise common events is quite rare.
However, assuming that their claim is correct, it is very interesting that the timing lines up with the solar eclipse which is itself, a very rare event. What I think is even more interesting is that this level of detail was remembered hundreds of years later when Homer was writing. That, by itself, suggests that something important happened and/or that Homer was working from a very detailed history of the time. Ignoring Odysseus for the moment, the fact that the timing lines up with the ash layer that is presumed to be the destruction of Troy is very interesting, and I believe that it lends a great deal of support to the historical fact of the Trojan war and more precisely, the destruction of Troy.
EDIT: to put it another way, I find it fascinating when literary evidence lines up with archeological evidence. It is rare to get two completely independent pieces of evidence in history this old, and it simultaneously puts the archeology in context while supporting the veracity of the writing.
The problem is, we do not know if it in fact happened on that day, or it was deliberately made appear more dramatic by claiming it has happened on that day.
We don’t know if Odysseus existed at all, and if he did many of the fantastic events in his journey obviously didn’t literally happen. Regardless, assuming the speculative interpretation of gods as planet locations in the sky is correct, this gives us a pretty good way to date the Trojan war. (Which we also don’t have conclusive proof happened, but anyway.. https://en.wikipedia.org/wiki/Historicity_of_the_Iliad)
It seems likely to me that Homer's works were amalgams of stories from the period of the bronze age collapse. During this time there was a broad spectrum collapse of civilization and power structures in the Mediterranean, and there was extensive raiding from groups of folks collectively called the "sea peoples" of which the Mycenneans almost certainly were a part. The "ten years" of Odysseus's journey is likely poetic license, but given that Troy was sacked and burned in 1183 BC and the eclipse occurred only 5 years later in 1178 BC it's quite possible that there were dramatic and memorable stories around both those events which circulated in greece around those times. And then during the chaos of the Bronze age collapse and rebuilding of civilization (which took about 2 more centuries) resulted in heavy embellishment and modification of those stories until they congealed into the pseuo-mythological forms they took on before being codified into oral history (which can actually have a high accuracy of retaining details) until Homer formalized them.
Reminds me of the book Hamlet’s Mill, whose thesis is that the main mythological epics from most ancient cultures were actually encoded astronomy https://en.wikipedia.org/wiki/Hamlet%27s_Mill
Popular fiction can make use of religious or historical elements without the purpose being to communicate religion or history. Consider the impression a future archeologist will have if the most accessible record of our culture is Netflix.
http://www.pnas.org/content/early/2008/06/23/0803317105.full...
from 2008, covered by the rest of press at that time, also by Scientific American.
An interesting response to it is (2012) by Peter Gainsford, a Hellenist who works on philology and mythology:
http://www.academia.edu/622261/Odyssey_20.356-57_and_the_Ecl...