The original mechanism has gearing to drive a sun/moon ecliptic display (in terms of the Egyptian (sothic) year, which the Greeks used, which could be adjusted against the zodiac display to adjust for leap days) including moon phases and adjustment for lunar ellipticity (moves faster half the month than the other half) and a 9 year cycle of elliptic precession). It ran a Metonic clock (translated the lunar calendar to solar, essentially) and a solar/lunar eclipse clock. Finally it has a small pointer indicating the year in the 4 year Olympic cycle.
The latest paper I've been able to find is from 2012 (
http://dlib.nyu.edu/awdl/isaw/isaw-papers/4/) by Freeth and Jones of the Antikythera Mechanism Research Project. It has been suspected that the Sun/moon display on the front had additional pointers for all the visible planets, which were run by gearing dissolved away while under the sea. Their motion would involve, of course, retrograde movements, so the gearing is not trivial ratios. This is the third proposal I know of to work out what that planetary gearing must have been; Michael Wright's physical model shown in the NOVA program was the first, and another was proposed by another team that required separate zodiac dials per planet. This third one also handles sun elliptical anomalies, since if they did it for the moon, the sun should have also been done. The picture of the front plate is striking:
http://dlib.nyu.edu/awdl/isaw/isaw-papers/4/images/figure04.jpg
Freeth points out that the accuracy presumed by inclusion of corrections for lunar and solar ellipticity would have been largely nullified out by the roughness of hand-filed gearing and the use of triangular teeth. Presumably these corrections were added because they were known and could be modeled, the physical reality be damned. Freeth also points out that during Mars retrograde motion the pointer could be as much as 38 degrees off the correct setting, but that was not because of the mechanics but because they had no good theory of the ellipticity of Mars orbit, and Ptolomy's
Almagest was still 300 years in the future. He notes that the use of circular gears for modelling required a good theory of epicycles, because that is precisely the model that has to be mechanically reproduced. Elliptical gears were just not in the cards

)).
I'm still wondering how they set the damned thing for, say, the day on which the manufacturing was complete. Setting the moon's current elliptical angle and angular velocity must have been a bear, let alone synchronizing all the retrograde movements to proper phases; then there's the five calendar pointers on the back. The guild of astronomers/mechanical engineers/craftsmen must have been a real wonk hangout.
It has been pointed out that Aristarchos had already theorized a heliocentric theory, and it is likely the people associated with the AM knew about it, if not believed in it. However, in 250 BCE, even then, Greek and Roman religious rigidity kept it a minority view and slowly squeezed it out of society. The AM (100 BCE) was likely the last gasp, stolen by the Romans and headed for a triumphal parade thrown by Julius Caesar when it rebelled and sank itself into the sea.
Sounds like a good opera scenario,anyway.