Give any Eastern Orthodox group a month or so and someone is bound to bring up the church calendar. Now, the calendar has two components: fixed feast/fast days which are tied to some civil calendar, and movable dates in the spring which are tied to the date of Easter. The date of Easter is determined by a Paschalion, a formula which is in turn tied to the coresponding civil calendar.
Back in the bad old days BC, Julius Caesar suppressed a lot of calendar abuse by forcing the Roman civil calendar into a fixed pattern of months and leap years, in order to keep the vernal equinox on March 21st. This Julian civil calendar was inherited by the early church. One of the issues decided at the Council of Nicea was that the church should observe a fixed paschalion as determined by the church of Alexandria. Contrary to much popular opinion, the current calculation was not dictated. That formula was devised a bit later by Dionysius Exiguus (who is also responsible for our current BC/AD dates) because the church in Rome needed a mechanical calculation.
Here I need to digress a bit. Everyone "knows" that Easter falls on "the first Sunday after the first full moon after the vernal equinox". The reason for this is that "the first full moon after the vernal equinox" should be the date of Passover, and Nicea decreed that Easter cannot fall on Passover. What the paschalion produces is a date for this first full moon.
The real moon isn't quite so cooperative. Both the Dionysian paschalion and the current Jewish formula follow a 19 year cycle of dates; but they don't use the same pattern and as a result there are years where there is actually another full moon between the equinox and Passover. The bigger problem with the Dionysian paschalion, of course, is that it is coupled to the Julian civil calendar. The Gregorian civil calendar was introduced to fix the drift of the calculated vernal equinox away from the real equinox; Easter as calculated in the Dionysian paschalion is in some years a month "late".
Now the Gregorian civil calendar could be accused of being a little inaccurate in that sometimes the equinox falls on the 20th instead of the 21st. Well, not exactly. See, it matters where you are. If the equinox occurs when it is noon in Japan, it is still the previous day in California.
You might think that the Dionysian and Gregorian paschalions should produce Easter dates that are either identical or are a month part, but they don't. The pattern of full moon dates isn't the same (accounting for the civil calendar difference).
A lot of people think it is a scandal that Christians can't agree on the dates of holidays, but resolving the issue has proven intractable. Catholics and Protestants have inherited the Gregorian calendar and paschalion; the Orthodox will not abandon the Dionysian paschalion unless there is uniform agreement to do so. Some Orthodox churches follow what is called the "revised Julian" calendar, which combines the Gregorian civil calendar with the Dionysian paschalion; they celebrate Christmas on December 25th (Gregorian) but celebrate Easter with the rest of Orthodoxy. This isn't really satisfactory, both politically and because the paschal season (Easter to Pentecost) falls too late in the year and thus runs into some other holidays and fast periods.
So is there hope? Tune in next time!