1 About that time King Herod [Agrippa] laid violent hands upon some who belonged to the church. 2 He had James, the brother of John, killed with the sword. 3 After he saw that it pleased the Jews, he proceeded to arrest Peter also. (This was during the festival of Unleavened Bread.) 4 When he had seized him, he put him in prison and handed him over to four squads of soldiers to guard him, intending to bring him out to the people after the Passover.It is commonplace among New Testament scholars to suppose that "Passover" refers only to 14 Nisan, the day on which the initial sacrifice is slaughtered. It is then followed by the Feast (or Festival) of Unleavened Bread, from 15-21 Nisan. On such an understanding you have a very strange narrative here, wherein James is arrested and executed either before or during the Feast of Unleavened Bread, followed by the arrest of Peter during the Feast and an intention to kill him after the Passover (it is not clear if the statement that this happened during the Feast refers only to Peter's arrest, or also to the arrest and execution of James. I suspect the latter, but the narrative leaves some ambiguity). In other words, on the typical usage, you would have Peter arrested between 15-21 Nisan, with Herod Agrippa planning on executing him once 14 Nisan was past. The only way this would work is if he was arrested sometime during 15-21 Nisan one year, held for a full year until the following 14 Nisan had past. This seems somewhat unlikely.
This problem disappears entirely if, with Pitre, we recognize that "Passover" can also refer to the entirety of the festal week i.e 15-21 Nisan. Then we would have James arrested and executed no later than 21 Nisan, followed by Peter's arrest sometime between 15 and 21 Nisan, with Agrippa planning to have him executed at some point subsequent to the 21 Nisan. The timeline is suddenly not a problem at all. Insofar as a hypothesis' capacity to resolve indirectly-related difficulties should generally be reckoned as confirmatory, Pitre's understanding of the New Testament usages of the term "Passover" seems to receive confirmation from Acts 12:1-4. (Pitre, incidentally, has indicated that Acts 12:1-4 were originally intended to be in chapter four of Jesus and History, but ended up on the chopping-room floor. Quite understandable: as it is, the chapter weighs in at over 120 pages. Sometimes one simply has to let things go).
Incidentally, as I am somewhat obsessive-compulsive about such matters, the events in question probably occurred no earlier than 41, the first Passover during which Agrippa had control of Judea, and no later than 44, the last Passover before his death. Based upon what we know about Peter's movements during these years independent of this passage, I am inclined to favour 41 or 42, with the former seeming more probable to me than the latter. 43 and 44 generally strike me as non-starters.