try this check the value is not empty before doing the operation.
$(function(){
$("#collapse1 #div_id_nested-1-birthdate input").on("change.dp change keyup paste click propertychange", function(e){
// get the current value and store it in the variable.
var value = $(this).val();
// checking the value is not empty
if(value.length){
var timediff = moment().diff(moment(value , "DD/MM/YYYY"), 'years');
if (timediff >= 67 ) {
$('#collapse1 #alert1').remove();
$('#collapse1 .panel-body').append('<div id="alert1" class="alert alert-warning">You are over 67!</div>');
} else {
$('#collapse1 #alert1').remove();
}
}
});
});