The ocean tides would still happen, but the bulge of water would follow the sun, so you could expect high tides around noon everywhere, everyday. I know some fishermen who would appreciate this.
Since the solid Earth flexes tidally, it makes sense that there might be some internal grumbling when Earth loses the moon. Earthquakes. Maybe a few volcanoes getting rowdy. That kind of stuff. But there’s no reason to worry (or hope) that California will fall into the Pacific. Sorry New York. Sorry Las Vegas.
The greater concern would be in the long-term, regarding the Earth’s wobbling spin axis. Right now the spin axis of the Earth very slowly wobbles over 26,000 years, like a slowing wobbling top, because of the tug of the sun. The wobble causes true north to not always point at Polaris, a.k.a., the North Star. Experts agree that the moon acts sort of like a shock absorber to this wobble — keeping it from getting out of hand (see the nitty gritty details in this SETI talk).
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