At 15k miles, odds are none of those items will need attention. Never hurts to have a look, but ethically, they shouldn't charge you for that inspection- they should be doing most of that every time they change your oil.
I worked at an independent Exxon station as a gas jockey, tire monkey, oil change clown... and I quickly learned to inspect most of those items while the oil drained from the car. When it's on a lift, the inspection is simple.
Here's what to look for:
Replace engine oil and filter
Rotate tires
Lubricate all locks / hinges - We did this at customer request, no extra charge. White lithium grease on hinges, very light spray of graphite powder into door locks.
Inspect the following:
Automatic transmission - Check fluid level on dipstick, look for discoloration of fluid as an indication of breakdown.
Axle & suspension parts - Visual inspection, look for bent control arms, etc. or hydraulic fluid leaking from shocks/struts.
Brake lines & cables - Look for rust, abrasion, wear, and signs of fluid leakage.
Brake pads, rotors, drums & linings - Check pad thickness, make sure rotor wear is relatively even, not deeply grooved.
Cruise control vacuum hoses - Check ALL vacuum hoses under hood & make sure they are not brittle, dry rotted, cracking, kinked, etc.
Drive shaft boots - Rotate drive shafts & look for cracks. Squeeze to make sure they are pliable, not brittle, dry rotted, etc. ***VERY important for FWD cars.
Exhaust system - Look for loose/broken flanges, hangars & clamps, excessive rust, holes in system.
Differential oil - Check level, make sure oil is not milky or runny.
Steering gear and linkage - Look for visual signs of wear, grab & tug to make sure everything is tight.
Steering linkage ball joints - Look for visual signs of wear, grab & tug to make sure they are tight.
Front suspension ball joints - Look for visual signs of wear, grab & tug to make sure they are tight.
Manual transmission oil - check level & make sure it hasn't gone milky, etc.
***Manual transmission & differential oil usually don't have dipsticks- you just remove the filler plug & stick your pinky in, about one knuckle deep. It should get oil on it. If not, you may be low.
And once you've done this a few dozen times- especially at a dealership where you're only working on one make of car, it should take you 5 minutes under the car & another 2-3 above. It can all be done in the course of a normal oil change. NOT worth much, if any, extra charge.
