Okay, first my own reactions, and then some responses to what's already been said.
The first order of business is to figure out where we stand, especially since the narrator is also the main character. Do we trust his version of events? I think Graves tries very carefully to give Claudius reasons for wanting to be honest. That doesn't necessarily guarantee his sincerity, though. He's a very textured character, and so far I like being in his head. Part of that texture, I think, is that he's intelligent enough to be suspicious of himself, to question his own honesty in how he relates the tale.
Several people have brought up the question of whether or not the book presents an accurate version of history. I think one interesting thing to note in regards to that is the tension Claudius himself raises when he contrasts official history with the sort of confidential history that he intends to write. I wouldn't say it's the purpose of that passage to clarify the question of the novel's accuracy, but it does open a few doors. If nothing else, you can point to it as an excuse for any deviation Graves might make from the documented, official history -- this is the behind the scenes stuff that doesn't make it into the official histories!
A couple of themes leapt out at me, and it might be worthwhile to keep them in mind as we read further: memory, reputation, honor. Power also seems to be a big theme, and it's interesting to me, so far, the differences between the people who want it but can't have all of it (Livia) and the people who don't particularly want it but are saddled with it (Claudius).
And then there's the Sibyl. This is interesting stuff to me, as it's a topic that I've read a lot about over the years. In fact, not long before I bought "I, Claudius" for this reading, I happened to have started reading a non-fiction history of the Oracle at Delphi, which is the prototype for our understanding of most Greek oracles and Sibyls. The author of that book, H.W. Parke, suggested that the Greek beliefs which made the oracle so popular were probably pretty alien to the Romans, so Claudius' visit to the oracle may be a little anachronistic. On the other hand, Claudius seems to have more than the usual respect for the Greeks, so maybe his view of the Sibyl is more antequarian than most. On the other other hand, Greece was held in high estimation by the Roman intelligencia in general -- that doesn't necessarily make any of them capable of the same sort of belief in oracles that a 7th century Athenian would have had. And so on, and so forth. In general, though, it may be noted that the Romans had a more systematic, almost mechanistic religion -- despite its similarities to and adoption of Greek forms -- which contributed to a general decline in the belief in and popularity of oracular pronouncements. So at best, we can say that Claudius' credulity is probably uncommon for an ancient Roman.
One cool little detail: there's an element of theatricality in the oracle, and it's something that Claudius himself notes, saying that the dramatic change in light was probably done by a neophyte on the roof. But despite his realization that the atmosphere is contrived, he still believes, to the extent that he has (apparantly) no doubt his book will be read thousands of years later.
Claudius interprets the Punic curse as the money-madness that's eating away at Rome's social structure. That could be Graves' analysis of the fall of the Roman Empire, but I wonder if he might not also mean it to reflect on us.
And does anyone know if there really were any such things as Syballine books with propecies that were taken to indicate the fortunes of the Caesars, or is that just a narrative conceit?
It looks as though a lot of the book is going to be about Poor Claudius' relationship to powerful and influential women. So far I count Agrippinilla, Livia, Octavia and the Sibyl. And one aspect of this relationship is that at least some of the women make use of the political ambition of men as a way of furthering their own ambition. The big example is the way in which Livia orchaestrated Octavian's transformation into Augustus -- that, I'm pretty sure, is ahistorical. But it's certainly literary, and Livia is in one sense the descendent, and in another sense the ancestor, of Lady Macbeth.
Another theme that crops up a bit in this chapter: piety. In particular, I'm thinking of Octavian's impotence with Livia, which Claudius attributes to his guilt over the impiety of their marriage; the belief that Claudius the Fair lost a naval battle from impiety; and the portents at Octavian's assumption of the name Augustus.
Another interesting religious detail is the creation of the gods Roma and Julius. And those probably are historical details, even though it seems like a contradiction to say that the Romans could feel pious towards god that they deliberately authored.