Boccanegra's plot has a mostly-deserved reputation for gloom and murk, and much of the murk stems from plots details in the play that Piave and Boito left out, changed, or obscured. Read Budden for some clarity.
And do yourself a favor and look up the Guelphs and the Ghibellines. The plot makes no sense whatsoever unless you know something about early Renaissance Italian political factions.
Lastly, the 1857 version is well worth hearing. There's this expensive commercial recording; in the early 80s, there was a live performance floating around as well.
Private to Dorothy Dunnett fans: Yes, Gabriele Adorno is from the same family that plays a part in the Niccolo books.