Technology is beside the point. All you have to be able to do is count days and see the moon a few times a month. What's impressive is the attention span, but more than that it's the conception, or apprehension, of the celestial movements.
Note though, that in 12,000 days the 365 day year drifts by about 8 days from the tropical, i.e. seasonal, year. This is a slow drift, and evidently didn't concern them, just as it didn't concern the Egyptians.
It's not that unusual, considering that a priest had not much else to do in his whole life. Nor he'd want to do anything else, seeing how other people live. Most likely priests were selected among smart and patient people. There was a short SciFi story about that.
This is a slow drift, and evidently didn't concern them, just as it didn't concern the Egyptians.
It wouldn't concern anyone as long as the priests correctly tell when to plant seeds and when to gather the crop. Since priests are aware of the drift this is not a problem. Thinking of that, the firm relation between months and seasons is not important at all; it's just a matter of habit. Ancient peasants weren't too much obsessed with counting of days, probably - even presuming that they knew how to count. Mayan calendar is not that simple. Chances are that the peasants knew nothing about the calendar and just used simpler terms (that are related to the agricultural or weather cycles) in their life. Priests would have every reason to keep their knowledge secret, as a job security.