Walk the area around the tank with a flashlight and a dry rag. Do not go looking for trouble. Go looking for a baseline. Look at the bottom of the tank, the floor under it, and the drain pan if one is installed. Look at every fitting: the cold inlet, the hot outlet, the drain valve, and the pressure relief valve. A dry tank with clean fittings is a useful starting record.
Signs at the base
Watch for a bead of moisture at a fitting, a stain line on the floor, a rust-colored crust at a joint, or a damp patch that returns after it has dried. Note the spot, its size, and the day you saw it. Repeated moisture at the base is a reason to call a plumber for an inspection, because the source may be the tank, a valve, or a connection, and each has a different fix.
Signs in the water
Water that runs rusty at the hot tap, especially after the heater has sat idle, can point to corrosion inside the tank or in the pipes. A sulfur smell in the hot water, or a rumbling sound from sediment when the burner or element runs, is worth reporting. Ask the plumber which checks apply to your system rather than assuming the cause.
The relief valve line
Check the discharge pipe from the relief valve. It should run to a suitable drain, and it should not be capped, kinked, or dripping steadily. Any water that drips from the relief valve is a reason to call a licensed plumber promptly. Do not operate the valve yourself unless the plumber shows you how it is done safely.
What to log for the plan
Keep a short log: the install year, the fittings you checked, anything you saw at the base, and any change in how the hot water performs. Bring it to the plumber and to your next planning review. Then ask the plumber what service life to plan around for your model, and let the log inform that conversation rather than replacing it.