You guys haven't done your homework.
The Mayan calendar was 365 days. The 5(,25) "leftover days" were added in some manner I don't recall. The years would be totally fucked up after a while of simply forgetting 5 days. No matter how advanced a calendar is, it won't escape the fact that it has to be 365,25 days to be properly in sync with the rotation of the Earth, both around the sun and its own axis. It's more or less pointless for anyone (especially a civilisation based on agriculture) to develop a time of measurement without the basic calendar that we have today.
As far as leap years go, I seem to remember that Mayans fixed this by adding several days (or something like that) every few years. I also recall something about children being born in these days were considered to be... well... useless. Most were sacrificed or simply mercy killed.
One or several of these tidbits may be incorrect, but I am absolutely positive about the Mayans have a calendar no worse than ours.
Peter Isotalo