For Jehovah's Witnesses, the "most important day of the year" is supposed to be the 'Memorial'. This 'sacred' event is to be held after sunset on Nisan 14. Except most of the time, it isn't.
As 'explained' in The Watchtower, 1 February 1976, page 73, the "governing body" (not capitalised at the time) takes it upon itself to 'determine' the 'actual' date of Nisan 14. They claimed in the article that the 'modern' date for the start of Nisan in the Hebrew calendar is calculated differently to the ancient calculation. However, that's not actually the case.
The actual calendation for determining the start of Nisan was (since at least the Neo-Babylonian period) and is based on the Metonic cycle - a sequence that repeats every 19 years.
In the Metonic cycle, the 3rd, 6th, 8th, 11th, 14th, 17th and 19th years have an extra (thirteenth) month (Adar II, or Veadar). This is added because the standard years only have either 353, 354 or 355 days (there are specific rules for this that I won't go into), so they lose about 11 days each year. Without the extra month, the subsequent years would start earlier and earlier compared to the solar year. The extra month is only added when the new year would otherwise start too early in what we call March, and the new year then starts in April.
Consider the chart below, showing two full Metonic cycles. The light yellow shading shows the years with an additional month. Green text indicates a correct Memorial date; blue text indicates Memorial date out by one day (either early or late); red text indicates Memorial out by a whole month. (Note that the Memorial date for 2015 hasn't been announced yet, but the JW date will be within a day of that shown.)
There are a few important things to note:
- Nisan 1 only ever occurs in April after a Metonic leap-year, otherwise it's always in March.
- Nisan 1 is never later than early April.
- When the cycle repeats, Nisan 1 for any particular year in the cycle is within a day of the same date in the Gregorian calendar (e.g. compare Nisan 1 of 1978 with 1997; 1979 with 1998, etc).
- The Memorial is always a month early following the 8th, 11th and 19th years of a Metonic cycle.
But it gets worse. Remember that year when the Memorial was in May? Yeah, me neither...
In The Watchtower of 15 November 2011, in attempting to defend their foolish 607 BCE dogma, the Watch Tower Society claims that Nisan of 588 BCE began on "May 2/3". Their dishonest footnote claims:
Therefore, the first Babylonian month (Nisanu) would have started the new year two months earlier, on May 2/3. While normally the year of this eclipse would have begun on April 3/4, VAT 4956 states on line 6 that an extra month (intercalary) was added after the twelfth (last) month (Addaru) of the preceding year. (The tablet reads: “8th of month XII2.”) Therefore, this made the new year actually not start until May 2/3. Thus, the date of this eclipse in 588 B.C.E. well fits the data on the tablet.
This isn't just an innocent mistake, because Nisan is the month of their most important day of the year, and they know that Nisan never begins in May. Their article claims that Nisan would "normally ... have begun on April 3/4", but they know that Nisan never normally begins in April. Nisan only begins in April after the extra month has already been added. (Specifically, the last day of Adar in 588 BCE was March 6, then there was the "extra month", which ended on April 4, and Nisan began that evening.)
So they're not just wrong. They're desperate enough to outright lie, because most good little JWs won't research anything, and many of them probably won't even read the footnote.