I bought a 2009 500Ri last November from a dealer after riding it for one minute in a parking lot.
It had 6.5k miles, an unknown number of previous owners, trouble starting and a check engine light.
Qualifies almost as "sight unseen". Price was good, came with extras so I bit the bullet.
What I did is just the basic maintenance whether it was needed or not:
Engine oil and filter, transmission oil, sparkplug, air filter, check the coolant, a bottle of Techron (or your choice of fuel system cleaner), check tire pressure, open the CVT and check if everything is in order.
I erased the code (it was an injector code) and it never came back.
The hard start lingered for a while but after riding about 1k, it seems like it's no longer there. the coldest start was at ~35F and it started almost instantly.
One thing I noticed though: if it doesn't start after half a second of cranking, it won't. What I learned to do is barely tapping the starter button (enough for 2-3 revolutions of the engine). Even if the battery is not too good, being patient and just trying this will eventually start it.
A (good quality) trickle charger HELPS A LOT if you don't ride it often. Both for starting and battery longevity.
Optional is "modding" the CVT. With stock variator, it seemed to have some flat sports in the rollers meaning it would "start in 2nd" and wouldn't "shift in top gear" (7k at 75mph and past redline before 85mph)
After installing the Malossi variator (and clutch spring), it changed significantly: it would "start in first gear" and it would behave a lot more like a CVT (full throttle would stay at 7k and smoothly accelerate). The highway RPMs would be ok (6-6.5k at 75mph).
Because I ride a lot on the highway without the need to accelerate a lot, I wanted something different. I installed Dr. Pulley 28x22 Sliding Roller Weights. What happened was just like changing to a longer final drive. Now it "starts in 2nd gear" but the highway RPMs are almost perfect (5.5k at 75mph). I would only recommend them ONLY if you do most of your riding on the highway.
Also optional is an aftermarket (larger) windshield (especially in cold weather) and one of those plastic "throttle control" thingy. Both very good on the highway, not that good in the city or small roads.
Other than that, there are small things like LED bulbs wherever possible, reconditioning the black plastics, greasing the parking brake mechanism, keeping it clean etc.