Checking out the state, city museums and even the Firenze Card, they do not have discounts advertised for over 65. However, that doesn't necessarily exclude some of the private museums - for example Palazzo Strozzi does have a reduced ticket price for over 65.
As for events, most discounts are connected to have a membership to places like COOP (an Italian supermarket) or a bus ticket for ATAF or sometimes even the train. You need to ask at the moment you purchase the ticket. I have rarely since any concessions made for over 65.