The Safari browser throws a RangeError instead of returning null when it tries to stringify a Date object with an invalid date value. The only reliable way to prevent this is to monkeypatch the Date.prototype.toJSON method as follows:

var _DatetoJSON = Date.prototype.toJSON;
Date.prototype.toJSON = function() {
  try {
    return _DatetoJSON.call(this);
  } catch(e) {
    if (e instanceof RangeError) {
      return null;
    }
    throw e;
  }
};

See https://github.com/angular/angular.js/pull/14221 for more information.