Here's how I would do it:

if (Object.prototype.toString.call(d) === "[object Date]") {
  // it is a date
  if (isNaN(d.getTime())) {  // d.valueOf() could also work
    // date is not valid
  } else {
    // date is valid
  }
} else {
  // not a date
}

Update [2018-05-31] : If you are not concerned with Date objects from other JS contexts (external windows, frames, or iframes), this simpler form may be preferred:

function isValidDate(d) {
  return d instanceof Date && !isNaN(d);
}