As requested, a picture of the calendar movement with some notes. Sorry about the poor quality of the dial photo, it's the only one I have to hand.
The calendar movement is actuated once per day via a drive rod (top left) from the strike train in the clock. The strike train has a disk with a pin on it that rotates once per 180 strikes (One day including half-hours - it is a pig to get to operate at midnight!).
The drive rod moves three actuators. A Day actuator that steps the day wheel on one day (7 teeth); a date actuator that steps the date wheel on one day (31 teeth) and a short month's actuator that moves every day, but only does anything once per (some) month. There is also moon phase gearing (the fine-tooth wheel is just visible) driven from the day wheel.
The months cam in the centre ( which also carries the central hand) resembles a count wheel. It is geared to the date wheel, rotates once per year, and has notches for the 30-day months plus February at 28 days. As pictured the follower is sitting in a 30 day notch.
At the end of the month, the pins (currently shown at bottom left) will have rotated (anticlockwise) round to be aligned with the face of the short months actuator. There are three pins one for 30 day months, one for 29 day months and one for 28 day months (hidden behind the setting wheel).
Depending on the month length the Month's follower lifts or lowers the Month's control lever which lifts the short months actuator to clear or catch the appropriate pin. In 31 day months the actuator lifts clear of the top pin and on the 31st of the month the date actuator rolls the date over to the 1st. In 30 day months the short months actuator catches the top pin on the 30th and pushes the date wheel forward 2 days to the 1st. In February of non leap years the actuator is fully lowered, catches the third pin on the 28th and pushes the date forward by four days from the 28th to the 1st.
Once every four years there is a cam on a wheel between the Months cam and the Moon gear which appears in the February notch and lifts the follower so that the short months actuator doesn't catch the 28 day pin - so the date goes on to the 29th, but the following day catches the second pin and pushes the date on by three days.
I have not dared take it apart. Getting all the wheels back in the correct relationships strikes me as a nightmare.
Hope this is useful to someone.
PS On the subject of leap years look up Julian and Gregorian calendars.