A long time ago I received some advice on buying a used car that I would like to pass on.
If the dealer offers you the opportunity to keep the car overnight, then drive it over various road conditions for at least 30 miles. Then take it home, park it in your driveway and ...WASH it. Get out a bucket of soapy water with a clean sponge and wash the car with loving care. You will be surprised by how many dings you will find by hand washing that you didn't see on the dealership's lot when you fell in love.
Open the doors and check for water leakage around the window seals and door seals and the sunroof . Open the trunk (boot) and check there for water leakage, also.
If everything is dry, you may have a keeper. If not, the car dealer will appreciate the fact that you cared enough for his merchancise that you actually washed it before returning it.
It's what some call a win-win situation.

They are all very good idea's. I identified straight away with the washing and loving care part.

I've bought many cars over the years where bodywork blemishes, rust, filled areas, and even a re-spray did not become apparent until I washed and polished the car.

I think, without exception, these have been private buys rather from those bought from dealers. I'm sure that there are many good private buys around but since I've come unstuck a good few times with them I don't buy privately anymore.

Working for an organisation which is frequently contacted when people have problems, we often have people who have bought a packet of trouble in the form of secondhand cars. I have never thought of telling people to wash the car although now you have mentioned it makes good sense. One thing we do suggest is, unless you are mechanically-minded, is to pay money for an engineer's report before buying the car, perhaps through a motoring organisation. It might seem expensive but could save you a great deal of grief and money in the long run.

Another tip is to carry out a check to find out if money is still owed by a former owner, if the vehicle has been bought on hire purchase (not sure what other countries call it but this is when the vehicle is owned by the finance company until the final payment is made) it could be that the person selling the car is not entitled to do so. The laws will differ from country to country but certainly in some places the purchaser would lose the money paid AND the vehicle if the seller doest't have good title.

In the U.S. the hire purchase is called a lease agreement. The dealership retains title to the car in all cases unless the lessee agrees to purchase the vehicle after the lease expires and pays for it, usually in cash or by re-financing.
There is only one title to any vehicle and that title must be transferred free and clear of any lien for a subsequent purchaser to obtain a clear title for the purpose of obtaining license plates or insurance.
Automobile titling is pretty straightforward since the vehicle can be positively identified by the vehicle identification number (VIN) which is prominently displayed on the vehicle and cannot be changed without damage to the VIN.