Don't worry about battery, they're the best in the industry.. and covered by 8 year warranty anyway. I have set my display to % charged, and just leave it on that forever. Never use the distance display (rated or typical) because I feel those create anxiety and can be misleading. (Get to know your own driving style and % consumption and you are golden, worry free.)
If the 2015 S85 range capability covers what you need on a regular basis you are fine, don't worry about range comparisons with newer or different cars, and don't worry about battery degradation. I mean, really, suppose your gas tank can only hold 95% volume of the gas you used to be able to pump into it... do you think that matters to how you use the car? It won't change a thing you do.
You should have free supercharging, check. Have the owner demonstrate SCing for you. Watch the whole experience carefully.
Take the car to public level 2 charger, try the J adapter. Dial up the Amperage on the car as high as it will go for that charger. Car built with dual chargers onboard? Then you'll want to see an Amperage over 40A to prove they both work so find a public charger that is rated above 40. Test out the UMC charger on a 240v supply somewhere.. maybe owners home.
I upgraded my 3G to LTE antenna in the car for $500... and I wouldn't recommend that change, not worth it unless you have way better coverage on LTE and need that.
Do all the traditional concerns about buying a used car, get a history on it. Get a quote for insurance on it. Do a trace on VIN with police for stolen property. Get Tesla's service records for it, from the current owner... if they can't produce anything assume nothing was done.
Have the owner login to their 'mytesla' account and show you anything you'd like to see, original documents, etc.
For this year of car, ask if the drivetrain has been replaced. Listen carefully to drivetrain for a test drive with no audio on, and windows up. Put the rear seats folded down for the drive and take all stuff out of the rear / trunk / hatch and lower trunk. If there are any issues you will hear whirring, screeching, clunking, etc at different speeds and accel/decel phases. You want darn near SILENCE don't accept "always been like that" answers for noticeable noises at the rear, anything other than what I'd describe as
very muted "electronics sound" similar to the classic defibrillator charge-up sounds you hear on T.V. shows. If in doubt, compare the drive sounds to a NEW Tesla RWD model only, not AWD, done at the store. AWD have more noises up front you won't have.
If you stomp on the accelerator and hear a high pitch balloon squealing sound emanating from what seems like "somewhere in the dash" don't worry about that, it's normal. And after 100K km on my car hasn't changed with new motor or old (my drivetrain was replaced). It's the go fast sound.
Oh ya, start strengthening your neck muscles doing some specific exercises, and have family members do the same. Or some will complain of whiplash driving around.
Buying a good used car at the right price is always more economical than buying new. You don't take the initial depreciation hit.
How long do you want to hang on to the car? Maybe plan on selling it in a year or two before the drivetrain warranty ends. These cars are retaining value better than most in similar class, so you can recoup something. Set your sights accordingly, knowing you're likely to get decent cash getting out of the car when you're done and haven't crashed it.
What's it worth to you? Is the only price you should feel comfortable offering. Set your maximum before you shop.