Consider using moment's hinting support:
moment(input, 'DD.MM.YYYY')
A Fiddle demonstrating the approach is available here:
Moment will assume local time inputs, so if you are working outside of that timezone you may want to append the timezone to your input. See the docs at http://momentjs.com/docs - in particular parseZone() and "String + Format" sections.
In the case of server-side (node), you are probably getting odd results because of the server's timezone.