date-validation.js

angular.module('myApp')
    .directive('dateValidation', [function () {
            'use strict';

            return {
                restrict: 'EA',
                replace: true,
                require: 'ngModel',
                link: function (scope, element, attrs, ngModel) {

                    function parseDate(value) {
                        // do your custom parsing here
                        var date = moment(value, "DD.MM.YYYY");
                        return date;
                    }

                    ngModel.$parsers.unshift(function (value) {
                        var date = parseDate(value);

                        ngModel.$setValidity("validdate", date.isValid());
                        return date.isValid() ? value : undefined;
                    });

                    ngModel.$formatters.unshift(function (value) {
                        var date = parseDate(value);

                        ngModel.$setValidity('validdate', date.isValid());
                        return value;
                    });

                }
            };
        }]);

gistfile1.txt

<md-input-container class="md-icon-float md-icon-right md-block">
    <label>My Date</label>
    <md-datepicker date-validation ng-model="mydate" name="dateField"></md-datepicker>

    <div ng-messages="newZaehlerstand.dateField.$error">
        <div ng-message="validdate">Date validation error message!</div>
    </div>
</md-input-container>