There's a lot wrong with Javascript's Date, but the fact that it's an object is is not really in the top 10.
Would it have been nice if the Date object had been immutable? Sure, but the fact that changing the mutable object does indeed change the object shouldn't be a shock
Would it have been nice if the Date object had been immutable? Sure, but the fact that changing the mutable object does indeed change the object shouldn't be a shock