Getting a package (Mail Room) also gives the date, but it's a bit unreliable (I got one that was "packaged and delivered on 11-5" the day before getting one packaged on 12-36, take of that what you will). Running payroll and picking up the payroll slip in the Maid's Quarters will show that it was payroll for the week of 11-8 (it always shows this date) which happens to be day 2.
Additionally there is a wall calendar in the Drafting Studio with Nov 7th marked as "Day 1"
The exact date is also next to the partition model of the Great Hall on the other side of the room. There's a slip indicating that that is the model is the layout for a specified date. That date happens to be the current date (the model and date are always accurate, with the missing wall side being the door the player typically enters from and is less ornate than the opposing door).
Additionally, in the vault, the desk has a block-calendar on with the current date displayed (so you can date your deposit slips).
