In many respects it's quite solid, and there's no doubt it was a move in the right direction, but it is out of date in a few important respects.

At the time, in the mid 20th century. for some decades there had been a habit of regarding the world depicted in the Odyssey as a more-or-less faithful depiction of the late Bronze Age. This habit was only strengthened by Parry's discoveries of the importance of oral traditional elements in Homeric poetry, which strengthened the impression that it was a tradition maintained continuously since the earliest times. It would be strengthened yet again by the decipherment of Linear B, which was announced a year after the publication of Finley's book: Linear B texts produced various vocabulary items and other features that made, for example, D. L. Page repeat again in his History and the Homeric Iliad (1961) that Homeric society was Bronze Age society.

Finley was a sane and healthy response to all this. He firmly cast Homeric society as a Dark Age society, and down-dated it to the 10th century BCE, contemporary with Protogeometric art. He also asserted the basic principle that the society depicted in Homer was a real one, with only minor distortions (something that was not, and still is not, universally agreed).

Nowadays, though, we've down-dated everything drastically further. No one now would dream of dating Homeirc society that early: it is mostly archaising to the 8th century, with some contemporary 7th century elements creeping in. It is on the whole real-ish, but with lots of intentional archaising which produces a few incoherencies. There are only a couple of elements, and a handful of phrases, which can be dated back to the Bronze Age; for the most part, the epic tradition as represented in Homer is very recent.

Finley's book remains a handy first intro, but there a few inaccuracies like these which may mislead a present-day reader. Another point against it is its ignorance of the contents of Linear B texts, something that has informed our understanding of the Bronze Age for over half a century now.