The PP is actually quite a timepiece. It tries to be a real analog to the actual motions of the earth, sun and stars. Note that the timepiece is 24 hours, rather than 12 hours, so the motion of the hour hand is an analog of the rotation of the earth instead of twice the earth. It even has a sidereal time setting which tracks the rotation of the earth wrt the stars, apparently with the map of heavens shown in the window. 30 and 31 day months are pretty easy to do, but February with 28 days and leap year every four years is a bit trickier to do mechanically.
I would guess the next level of complication may not be included in the watch, although it has been well known for several hundred years. That is, that the length of the solar year is not 365.25 days (which gives the leap year every four years), but actually 365.2422 days, which means that we don't need leap year every four years. This was solved by skipping 3 leap years every 400 years, so century years, which should always be leap years (divisible by 4) are not leap years unless they are divisible by 400. So 2000 was a leap year, so was 1600, but 1700, 1800, 1900 and 2100 etc. are not leap years.
That means that the watch owner will have to return the watch to PP in 2100 to get it set properly for the date-day. Just in case PP did correct for the 3 leap years in 400 years problem, the actual leap year goes off that calculation in about 8000 years (IIRC).
BTW, this got resolved by the Pope back in 1582. However, Henry VIII had taken England out of the Catholic Church by then, so England stayed on the every 4 years leap year for another 200 years and England was out of sync with the rest of Europe for that time.
More interesting is that the first really expensive clock was built by John Harrison in the 1700's with which he won the Longitude Prize (look it up in Wiki) and received the equivalent of about $4-5M in today's dollars. Now that was something! You can see several of Harrison's clocks at the Greenwich Observatory near London.
Larry
PS. This and more was all in my calendar lecture in my basic astronomy course I taught for almost 30 years.