There are plans to adapt the jQuery UI Datepicker widget for use in a jQuery Mobile site. At the time of this writing, the widget was still highly experimental. When a stable version becomes available, you might prefer to use it instead of the following solution, which checks only the date format, not the validity of the date.
This solution uses a complex regular expression. Copying regular expressions from printed books often leads to mistakes, so I suggest that you copy the code for the regex from reservations_date.html in ch06/complete.