This is a tough one. I'll add as much fact mixed with a dose of opinion as I can.
1) Unfortunately, most people are out to cheat you. It's a cultural thing where dishonesty and cheating others is not really seen as morally wrong but as a healthy way to beat the system or to get one up on "them". Though your average Peruvian is incredibly polite and friendly, and when he wishes you all the best he really means it, but if he can sell you a S/.3 bottle of Inca Kola for $1000 he will.
When buying a used car this means you'll have to be careful. Unlike other countries where of those selling a used car 50% are doing so merely to trade up to the latest model and there's nothing wrong with the care, and the other 50% are doing so because they know they have a junker... in Peru is more like 80% are selling because something is wrong with the car and they don't want to fix it, the other 20% are selling their car because they need the money to pay off something else. It may or may not be in a "good state", and a "good state" means it works ok but had never undergone the maintenance it should have. This is true even if buying an expensive car from a millionaire who bathes in virgin olive oil.
When asking why they are selling a car, they will always say they are leaving the country, or moving city because of work (the same is true with traspasos of businesses). In truth, the car is old, has never been maintain and you're going to pay 20-50% the value of the car in repairs to pass the next revision tecnica.
2) To your favour, if a seller was a rare one who did do maintenance, who recently replace the "this" "that and the "other", no-one is going to offer him a fair price, or cover the value of the work he did. This is Peru and everyone wants something for nothing and has nothing to pay with anyway!
3) Before buying any car, find a mechanic (if not multi-marca, better), introduce yourself, and tell him you will bring a car or two for you to look at before you buy one. If he tries to offer you a car, refuse it, if he insists, find another mechanic who instead has your interests in mind.
When choosing a car, explain you want your mechanic to check it over. If this is met with a "but the car is fine", find another car.
4) It's unlikely that you'll be able to pay with a bank transfer, unless the guy happens to be with the times. Many people are not with the times and want cash.
5) The process is as such:
a) Find a car, check it with mechanic, agree a price based on findings
b) Check the car is in the guys name, and not in the name of his dead cousin's friend.
c) Go with them to the notaria. If you are given the keys, hand over the cash. If not, pay on delivery of car rather than before or in notaria.
d) You need to pay for the transfer of the tarjeta de propiedad, AND for the notaria to look into the multas the car might have attached to it. If you buy it with $100 of fines, you will be liable to pay them.
c) Peru recently changed the licence plates on cars. The notaria will tell you about this. It involves a little extra work in that you have to go to caminos de inca (i think) to pick them up and screw them on. You then have to go back once more to get the RFID sticker for your windscreen.
d) You can drive your car around when you don't have your plates because you'll have a special document, BUT you DO have to wait until you have your tarjeta de propiedad (3ish days).
6) With the revisiones tecnicas still in the early stages, it is still possible to tell for 99% of cars when they need the revision by looking at the last number of the licence plate, but you can get the checks any other time and get out of sync. so far this year, 1,2 and 3 have been revised. Next month is 4.
If the car is due a revision and they are selling it now... bad sign, they know there's something expensive to fix. Try to buy a car that passed recently.
7) Money saving tip. There are tonnes of used car places, especially on Aviacion, Benavides, and Angamos. Believe it or not, but each of these is marked up by as much as 20% what they owner, who leaves the cars there for the guys to sell, really wants for it.
You will find a car in El Comercio for say $5000. The showroom sells it for $6500. Nuts if you ask me. But in Peru there are lots of people who simply have too much money and are very lazy. Buy directly from the owner.
8) Some makes and models are more likely to be stolen than others. There are lists published by the police. The car doesn't have to be new or even look in good condition for it to be stolen or stripped down. This is evidenced by one of the top three stolen cars in Lima being old Volkswagen Escarabajos (Bugs).
Some cars bring out a more violent streak in people... drive a Toyota HiLux and you get viciously carjacked. Drive a Toyota Rav4 and you won't, but it will be stolen when you're not looking. Odd.