The sad part is these days that even so called 'safe' well known big name dealers can sell you a car with the mileage turned back. If someone has kept the clock mileage within the previous year MOT mileage, it could easily have been hammered for 50k miles or more as a rep car and the clock turned back 49k before it was part ex'd to a major garage.
If the car has been crash damaged but not bad enough to economically write it off it will not show on the search data bases as a write off. However you could have problems with the suspension on one side being tight, and it corners ok but is out of balance when it goes into a bend. You could have a cracked or slow leaking radiator. Many odd problems with headlight alignment or load levelling systems.
If you have doubts that a car for sale is showing a lower mileage than it should (and the Govt MOT history checker bears this out) then contact the trading standards office for the area where the car is for sale and report it. If you are paying significant amounts of money for a car get an independent mechanical check on the car (even where there is a garage warranty) A warranty is only worth something while the garage is solvent and trading (and even then it can be nearly impossible to get recompense) If the garage goes out of business the warranty is worth diddly.
Look at a car very closely around the bonnet - the gaps around the headlights and the bonnet should be constant and absolutely true to the mm. Look at all the paint on the panels and look for any slight shade discrepancies in the paint work (matt areas or areas with change of texture) Look behind the petrol flap or a change in paint colour. Check under the bonnet around the edges. Drive the car on a quiet straight road - and when the road is clear gently release your grip on the steering wheel (it should not wander to one side of the road or the other) When you press the brake pedal it should brake without pulling to one side. There are other engine gearbox checks you can do. When the car is in a safe place, chocked and secure check around the brake discs & pads for brake fluid leaks. Look under the spare wheel in the boot insert and see if there are any signs of ripples (rear end shunt damage) in the floor panel. Check around the rear light lenses for signs of misaligned panels.
You have to use your gut feeling on a car (if you have any mechanical knowledge) You can hear engine or mechanical issues if you are used to understanding an engine. Squeals, ticks, shudders. ~ An engine should quietly purr - a manual gearbox should move through the gears without difficulty and not jump out of gear; an automatic gearbox should not lurch violently. Look for fault icons on the dash. Engine management lights - typically an EGR valve fault or oil loss into the catalytic converter.
Make sure the car has a V5 registration document. Check the chassis vin (usually in the area below the front n/s of the windscreen) Sometimes in older cars it is under the carpet alongside the driver seat. Do a search engine search to locate the ID marks for the make & model of car you are buying. See the car at the address it is registered to. If you can verify the engine number against the V5, take a torch (but even then this can be difficult to see)
Remember your little old lady could be a 'disarming' front for selling cars from someone else or a garage which needs a bit of a sales boost.
So take someone with you to inspect a car for sale. If it's a runner it will just drive and hopefully have an MOT as well (if you are lucky it will be roadworthy) Trust your instinct. If it runs like a bag of spanners, the engine ticks loudly or runs with thick blue smoke walk away. You just can't polish a turd no matter what.