Hm, I think that there were natural philosophers who have a better handle on alchemy than we do now. 
The purpose of our current calendar is to keep the days of the year in the same season every year. Without a even number of days in the solar year and a desire to keep track of time using the day night cycle leap days need to be added.
The Maya did not feel the need to match their calendar to the seasons. Their calendar just counts days. It does not really concern itself with solar years and thus does not need leap days.
And don’t forget that back when we all ate mouldy vegetables and rotten meat instead of all this processed food, and nobody took drugs made by the evil pharmaceutical companies, hardly anybody died of cancer!
(Because they mostly died of dysentery and malnutrition, or from diseases that are now easily treatable, before the cancer had a chance to take hold, but we’ll leave that part out.)
I’m tempted to tell Mayan doomsdayers that they can avoid the apocalypse by doing what the Mayans did–sacrifice a virgin daughter–if there weren’t the chance of them taking it seriously.
I’m assuming that, since you added that part about the “Ancient Aliens” show, this was meant to be sarcasm. Nevertheless, in the spirit of fighting ignorance:
This page seems to be a pretty detailed explanation of the various Mayan calendars. None of them account for leap year. The Haab is 365 days, and the Tzolkin is 260 days. And as has been already stated here, the long count calendar isn’t cyclical, it’s just a straight count of days, so the length of the year isn’t even relevant.
All you people dissin’ the Mayan calendar just need to remember the following:
So, you know, take THAT!
The newest Mayan calendar find will take us 7,000 more years to reach the end.
The Mayans had several different types of calendars and none of them were necessarily synchronized. The Mayans most likely did not create the calendars they were using at first and more than likely inherited them from previous cultures.
The calendars that the Mayans used were fairly accurate for the time when they were created. Their calendar is nowhere near as accurate as the Julian or Gregorian calendars. The Mayan calendars averaged one day of error for every four years. Julian calendars had one day of error every hundred-or-so years.
The calculations that supposedly determined the date of December 2012 might have taken into account Gregorian leap years but they more than likely did not include the error-days in the Mayan calendar or other events such as the Calendar Act of 1750 where a few months were just ‘skipped’.
It should also be noted that the ‘end of the Mayan calendar’ is not defined by the creators as being a cataclysmic event. It is just the end of a cycle. It is basically like New Year’s Day. People who are talking about cosmic alignments and whatnot fail to tell their believers that cosmic alignments of one sort or another are actually not so uncommon as to be seen as miracles. They can happen several times in a person’s life or yearly depending on what you’re looking at. Most people alive today have been though a ‘cosmic alignment’.
Anyone attaching some apocalyptic significance to December of 2012 will fall by the wayside just like the dozens or hundreds of others who previously predicted the end of the world. The world will not end, spaceships will not descend and the reptilians will remain in the hollow center of the Earth. Nothing to see here.
You’re hand waving over one of the most brutal pogroms in the history of the world. How were the potential sacrifice victims better off by being massacred by the Spaniards? In any case destroying their records was just pure xenophobia, and robbed anthropologists of a rich treasure trove that they’ll never recover.
Even better: Stargate-SG1 (Season 3 Episode 21)!