Yeah, you can drink a day-old shot of Espresso. But by doing this, you will certainly get the point that it is not OK. As the taste of day-old Espresso will be very bitter. No, the espresso shots do not expire, so it will not affect your health at all. The taste of Espresso gets bitter with time. So, it's better to store leftover Espresso in the fridge for the time and make some milk-based drink with it. The sugars present in milk suppress the bitter flavors of old Espresso and make it drinkable.