Let's take a look at the two calendars most relevant to New Testament chronology
Julian Calendar
When implemented the Julian calendar was a significant step forward in chronological accuracy, pegging the tropical year at 365.25 days (just a little over 11 minutes off). There was a problem though--they accidentally held leap year every 3 years instead of every 4 for several years (I'd hate to have been the Imperial chronologer when Caesar found out about that). The exact date when this was corrected is a matter of some dispute, but the calendar was put right prior to the death of Augustus (AD 14). See here p. vi & p. 34 for a quick review of the history I've cited).
This means that errors in the Julian calendar are relevant to a discussion of the events of the Nativity, but are not relevant to the chronology of Jesus' ministry or death; the Julian calendar had been corrected by that time. In my own work on the chronology of the life of Jesus I use calculated Julian dates rather than observed Julian dates in order to avoid this obstacle.
Summary: The error in the Julian calendar, though real, has no impact on passion week chronology.
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Jewish Religious Calendar
(not to be confused with the Jewish civil calendar)
There is some grounds for belief that the date of Passover was subject to "off-by-one" errors during the period covered by the Gospels. I do not consider myself an expert in the details covered by the book by Humphreys (cited in the OP), but I can refer you to a Jewish source explaining why sometimes different groups of Jews observed the Passover feast on different days--see here.
In a nutshell, because the beginning of the month was determined by the observation (not the calculation) of a new moon, as validated by the Sanhedrin, Jewish communities would have to wait for word from the Sanhedrin when the month of Nisan had officially begun so they knew when 14 Nisan was, and could observe the requisite rites on the right days of the Passover week. The trouble was this: some Jewish communities were more than a 14 day journey from Jerusalem and so wouldn't get word from Jerusalem in time.
A lunar month can be either 29 or 30 days in length, so as noted by Dreyfus (article linked above)
They could narrow the possibilities to two days. So to play it safe,
they started observing each yom tov for two days, so that one of the
days would be the correct date of the holiday (as determined in
Jerusalem)
This means an off-by-one error could indeed exist, though it would be more likely to occur far from Jerusalem than within Jerusalem itself.
Talmage points out yet another possibility, which has the advantage of being (at least by implication) supported by Josephus:
[I]t is held by many authorities on Jewish antiquities that before,
at, and after the time of Christ, two nights were devoted yearly to
the paschal observance, during either of which the lamb might be
eaten, and that this extension of time had been made in consideration
of the increased population, which necessitated the ceremonial
slaughtering of more lambs than could be slain on a single day; and in
this connection it is interesting to note that Josephus (wars, vi, ch.
9:3) records the number of lambs slain at a single Passover as
256,500. In the same paragraph, Josephus states that the lambs had to
be slain between the ninth and the eleventh hour (3 to 5 p.m.).
According to this explanation, Jesus and the Twelve may have partaken
of the Passover meal on the first of the two evenings. (Jesus the
Christ, p. 618)
This too could create an off-by-one error, and this problem would be specifically felt in Jerusalem itself.
Summary: Surviving sources do not definitively answer the question in the OP, but an off-by-one error impacting chronology during Passion week is plausible.
