The one thing I'm pretty sure we can't change about Date is its representation in encoded form (usually as a Double, in property lists or keyed archives). Even if we choose to change its underlying representation to be integer based, or Int128 based - we still have to read it in and write it out as a double, which will almost certainly result in the same kind of precision errors described here.
@scanon has actually been looking into what options are available here for Date's representation.