First off the tides would be larger, stronger, and more difficult to predict (but not impossible).
It also matters where the second moon is. Is it the same distance as the moon? If so this could result in a collision which would cause debris to reign down.
If it’s not the same distance then we’d get to enjoy two moons. The earth would probably be a bit more bulgey around the middle.
Night would also be brighter, with the greatest brightness being when the moons are both full. If their cycles allowed for this.
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