1) As you enter the apartment start looking/inspecting the overall condition of the apartment (walls, floors, ceilings, windows, doors, etc). The other should be in a similar condition to what it was when you first visit it.
2) The apartment should be at least broom-cleaned with all sellers' items removed.
3) Open & close the windows and doors.
4) Turn all light switches on and off to make sure they are working.
5) Bring your cell phone charger and test all electrical outlets.
6) Test all kitchen appliances to make sure they are in working condition (microwaves, dish/washer, fridge, stove/oven, etc).
7) Run the exhaust fans (if present) in the kitchen and bathrooms.
8) Open all cabinets, closets, storage spaces
9) Run all sink and bath faucets as well as the shower, and check for any leaks or other problems.
10) Flush toilets and look for drips, leaks, or problems.
11) Test the A/C and heater units (it could be hard to …