Other mistake: In the cave we see Tom Hanks drawing an analemma without a precise timekeeper, which is needed to draw one. What he could have done is a meridian rect, which is build with the meridian time. The analemma is the differential chart between the solar time and civil time.
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Suggested correction: No, what we see is Tom Hanks drawing a chalk outline on a wall to approximate the date. There is no reason to assume he got it exactly right or knew exactly what he was doing. He probably started just by drawing lines on the cave wall to mark the days then noticed the light.
Greg Dwyer
I'm afraid "just drawing lines" doesn't create the well-crafted analemma you see in the movie. A very precise time-keeping device is necessary: just a minute off will dramatically change the shape.