Umberto Eco's large oeuvre can be divided into four groups: his scholarly work on semiotics, his amusing essays and plays on genre, his fiction, and his works for the mythical "general reader." This last group, to which Serendipities belongs, is the least effective and worthwhile, and this book is not a major contribution to that group.
Let's begin by assuming that you are interested in the history of language, intellectual history more generally, and/or the history of folly (or "lunacy," as Eco calls it). If none of these fit you, you won't probably like the book much; but let's assume you are so interested.
Serendipities is a group of five short essays about various oddities of European intellectual history as it relates to ideas about language. If you have read Eco's The Search for the Perfect Language, this collection is a sort of addendum, unfortunately rather repetitive. If you haven't, you will probably have little context into which to fit these discussions of Athanasius Kircher's theory of Chinese characters and Egyptian hieroglyphs, Leibniz's binary-mathematical interpretation of the Yi Ching, etc.
Assuming, however, that you have that context --- and note that we are now talking about a very narrow audience indeed! --- you will find a number of amusing bits of trivia, but little analytical depth. One has the sense that Eco is describing some little bits of things he stumbled on, which might be interesting to follow up but which are, for him, tangential or marginal.
The most valuable discussion in the book is the first chapter, which considers the problem of a history of folly. What are we to do when we encounter an extremely influential set of ideas based upon an entirely incorrect premise? For example, the Donation of Constantine, or the existence of Prester John's Christian Empire of the East, or the existence of the Rosicrucians, etc. --- all of these influential ideas are based upon some massive misrecognition, some completely erroneous interpretation of the authenticity of some text or texts. So how are we to interpret that historical influence?
It is an interesting and important question, closely allied to the problem of a history of magic or the occult. Unfortunately, Eco does not attempt a methodological solution, but rather places these ideas into their respective historical trajectories and points out how influential and odd are the conclusions drawn.
But so what? If you think it's great fun to expose the confusions of our intellectual ancestors, and have the background to understand specifically linuistic confusions of this sort, you might find this book enjoyable. For certain it is well written and charming, after all. But as for any conclusions, well, Eco doesn't draw them. As such, this is more or less a list of things which would ordinarily be found in footnotes to abstruse scholarly works. And without a serious and in-depth analysis, they should go back there.
If you are a big fan of Eco in all his genres, and thus have read and made sense of a good deal of his serious scholarly work (e.g. his Semiotics and the Philosophy of Language, or The Limits of Interpretation), you will probably want to add this to your collection. Otherwise this is not the place to start with Eco, and probably not the place to end either.