The current Western calendar system we use is a mess, and I think that the international adoption of its use was one of the worst decisions of human history.
For international use, we should have adopted something which makes much more sense and logically useful. Personally I think that we should have kept Chinese or Iranian lunar calendar, that is more logical and astronomically better designed, which also noted the precise days of the solar cycle events by any rate, for agricultural purposes.
The problem was, of course, the lunar events (moon day and month) and the solar events (solar day and year) did not match in their timings, e.g. "start" and "end".
The current Western calendar uses Month, which was based on the phases of the moon. Since the calendar is not based on the Moon phases anymore, the use of the word Month should have been abandoned.
Some of the month names are based on the Roman counting system. September (7), October (8), November (9) and December (10). Since they are not meaningful anymore, we should have abandoned such practice that is meaningless in modern days.
Since the time of the day is a solar event, the noon is meant to be the time when the sun is at its highest point in its orbit in the sky, ignoring the current observation of regional "standardized" time. However, the moon can't be always precisely full at midnight of the full moon day.
Also, the weeks are based on neither solar or lunar events. For international use, I think that they should not have been used at all. Old lunar calendars used either lunar (the first day of the month, first quarter, second quarter full moon, etc. and the last day of the month) or decimal (10th day of the month, 20th day of the month) to mark holidays etc. Holidays based on the 10 day cycles make more sense than weekly cycle, except that the full moon nights seem more adequate for some nocturnal celebrations.
The lunar calendars noted solar events as, e.g. equinoxes, solstices, seasons. They do not fall on fixed dates on the lunar calendar every year, but that is hardly a problem, since the exact dates can be calculated precisely in each year. From the way the old Roman calendars were made, it does not sound that early Romans did not possess precise astronomical knowledge to make this work well.
Instead of having the shortest month (February) and the leap year, etc., the lunar calendar had to have the 13th months sometimes, but I think that it is still better to have the 15th days of the month coincide with full moons.
Also, apparently Christians argue whether their "holy" day should be Sunday or Saturday. This argument is ridiculous. Which day is the 7th day is totally man-made affair. Neither day has any divine or astronomical significance, since the calendar system we use is not sanctioned by their god by any rate. This argument is one of the idiocies of Christianity.
