The basic problem Humphreys wants to solve in this well-intentioned book is that of the conflict between the Synoptic Gospels (Matthew, Mark and Luke) and the Fourth Gospel, of John. While the Synoptics share a chronology where the Last Supper is a Passover banquet (see Mark 14:12-16 etc), John's Gospel has Jesus' death take place on the day before, when preparation for the feast was taking place, and so Jesus is arrested, and already before Pilate, before the banquet could have happened (John 19:14).
Humphreys suggests that the problem can be dealt with through harmonization of the accounts; that is, with enough scrutiny and thought, the contradiction is not so much resolved as removed, because both accounts were true. In this case, the solution is a supposed variety of calendars being used in first-century Judea. This isn't a complete impossibility by the way, nor is it a new theory. The discovery of the Dead Sea Scrolls in the mid-20th century gave impetus to the idea there really were different calendrical systems in first-century Judaism. Annie Jaubert's study, published more than half a century ago, addressed the same problem and offered a vaguely-similar solution.
What James Vanderkam states gently but devastatingly about Jaubert's theory, however, is just as applicable to Humphreys': "there is no evidence that Jesus or any early Christian of the New Testament period used the solar calendar of Qumran - or any other calendar that made them noticeably different from other Jews" (The Dead Sea Scrolls Today, 214-5).
Mark Goodacre has made some of the important points about the false problems in Gospel chronology at his NT Blog. Worth emphasising too is Humphreys' tendency - not unique by any means, but unsatisfactory nonetheless - to retroject evidence from later Rabbinic literature (e.g. about the times of trials, or the use of water-jars) as though it gave an accurate sense of first-century belief and practice.
These and other technical problems with the execution of the argument would probably be sufficient grounds to pass on quickly. However I think the more serious problem is not technical but hermeneutical or theological, and needs to be described a bit further.
Humphreys' account suggests "all four Gospels agree on the date and nature of the Last Supper" (p. 193). This is a sophisticated example of how fundamentalism subverts the Gospels by deconstructing them in favour of some supposed "fifth Gospel" that lies behind the texts, the "real history" of Jesus' last days. In fact the Christian Church offers these problematic texts themselves as the bearers of meaning to those with ears to hear. They exist to be read and heard, not to be mined or deconstructed for that sort of "scientific" truth Humphreys wants, but whose pursuit can make him sound like someone who has never read the Gospels at all.
Despite assumptions to the contrary, such attempts at harmonisation represent modernity, not traditional Christian interpretation. The ancient Fathers of the Church understood that not everything in the Bible was literally true, but were relaxed about it; they were interested in more important stuff. In the third century Origen of Alexandria, the greatest biblical scholar of the early Church, commented on the different chronology between John and the Synoptics:
The student, staggered at the consideration of these things, will either renounce the attempt to find all the Gospels true, and not venturing to conclude that all our information about our Lord is untrustworthy, will choose at random one of them to be their guide; or will accept the four, and will consider that their truth is not to be sought for in the outward and material letter (Commentary on John, 10).Indeed. As far as the stories of the Passion are concerned, the cost of missing this point is profound. The Synoptics present Jesus eating the Passover with his friends, taking the symbolic bread of the meal and saying "this is my body". His Paschal self-identification is clear and startling. In John's Gospel however, Jesus dies on the cross at the time of day when his near-contemporary Josephus says the lambs for the feast were slaughtered (Wars 6.9). They do not say the same thing, in Humphreys' sense.
The only thing a historian is likely be convinced about beyond reasonable doubt regarding the chronology is that Jesus' death coincided with Passover; to insist on more is as pointless as it is groundless. If some new discovery awaits to make us think anew about the chronology of the Passion, Humphrey's work isn't it.
Yet it is the same story, across all four Gospels, in another way. Many hearers of the stories will continue be convinced about far more concerning Jesus from those conflicting accounts than chronological harmony could possibly convey. The real harmony lies not in historical agreement, but in their common witness to the one whose passion they recount.