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DaveP: With all that water sloshing about, might it not affect the balance of the Earth and make the ancient almanac useless?  Asking for a friend.

LOL, Dave. I think you and I have the same friend. :D

Depends on how far in the future that movie is set. Wikipedia says it's set in the year 2500, but in the footnote it explains that this is a production rumor (which is another way of saying it doesn't belong in the article!). Based on the evidence of surviving technology and stacks of National Geographic magazine, and yes, a sextant from maybe 1925, the setting is about a century from the moviemaking date. Call it 2095. That's not far enough in the future for the re-arrangement of all that water to make a difference measurable in celestial navigation (even the exaggerated amount, about 100 times more than possible even with complete meltdown).

But yes, melting the icecaps would change the Earth's rotation. Not the axial tilt, which would be largely unchanged, but conservation of angular momentum would slow the Earth's rotation even more than expected from lunar tidal friction. In the world today, huge masses of ice are located in Greenland and Antarctica. Those huge masses are close to the Earth's axis. Melt those and the mass will re-distribute more uniformly around the globe. It's the figure skater thing in every Physics 101 textbook (and youtube video)... moving water from near the poles out to the equatorial regions is like a spinning ice skater stretching arms out. The rotation rate decreases to conserve angular momentum. It's not much but if the astronomers move to that Dryland around the former Mt. Everest, they could detect it.

Tell your friend. Still LOL. :D

L.A.M.