A full senior check-up should include bloodwork to check thyroid, liver, kidney and blood glucose values (usually there is a specific senior panel, but verify that it included T4 levels). It should have a physical exam to check for any abnormalities, including arthritis and dental problems. A urinalysis should also be done to check for signs of kidney problems, diabetes, or urinary tract infections. If the cat goes outside, FIV and FeLV tests might be recommended, along with a stool check to look for parasites.
I recommend getting copies of any test results each time so you can keep track of them. Keeping a record of your cat's weight is also helpful in looking for changes.