Rust - I always think of Neil Young's "Rust Never Sleeps."  Avoid any car with rust.  If it's beginning to rust, it won't stop.  Be wary if you see rust repaired and painted over.  Unless the rust holes have been metal-patched by a skilled auto-body craftsman (rare these days), the rust will come back, usually within a year.  Look for rust at the bottom of all 4 doors, both inside and outside, and underneath.  Bubbles near chrome or rubber molding indicate rust underneath the paint.  Rust problems on a late-model vehicle are a tell-tale sign of a previous accident.  If a car has any visible rust, you can be sure the underside of the car is in worse shape.  Rust adds hundreds of dollars to your maintenance bills.  It may take a mechanic twice as long to do simple tasks because a rusty bolt breaks off in the course of a repair.  If you detect any rust on a prospective purchase, look elsewhere.  

Accident Damage - If you're not using a mechanic, don't buy a car that has been in a serious accident.  Significant accidents bend the frame, mess up the alignment and loosen the body.  Even a serious fender bender can mean major trouble in the long run.  If a car has been in a wreck, look for another.  Learning to be an accident detective is the best way to avoid the problem.  Sometimes the repair work is very good, but usually it's just cosmetic, with major defects remaining underneath the fresh paint.

Make sure you open the hood, trunk and all four doors: they should close easily without catching.  A sticking door or a hard-to-close trunk suggests a car that's been hit.  Sight down the side of cars to see that the sheet metal matches up evenly.  Squat about 6 feet away from the front or back of a vehicle and you're likely to see ripples, waves, and ill-fitting panels on the side that has been repaired.  (Don't confuse body waves with door pings, which aren't evidence of body damage.  A door ping will look like a dimple in the sheet metal, whereas waves and ripples are broad.)  Serious damage shows up in irregular body seams and exposed welds inside the engine compartment or underneath the trunk.  To check the frame, get down on your hands and knees with your trusty flashlight and shine it on the underbelly of the car.  Pay particular attention to the frame rails, the thickest-gauge metal rails going the full length of the car, usually on both sides.  Shine your light on it all the way up and down.  Check it from both sides of the car.  You're looking for anything that doesn't look right, like metal that is bent, or weld marks, which look like melted metal.

Late-model vehicles with new paint jobs have usually been in an accident.  Most repainted cars are repainted because the owner received a check on his insurance claim from an accident; rarely because someone has an extra $1,500 lying around.  Look for differences in paint color, sheen or texture.  Check to see that the color and finish of the car is consistent from panel to panel.  If the car was repainted, it usually doesn't take long to find where the tape didn't cover a sliver of the window seal or weather-stripping.  Look under the hood, in the doors, wheel wells and trunk for signs of overspray (specs of paint that are the wrong color).  Look closely around all the window seals and lights and other trim.  Also look for shiny new bolt heads and bright new trim pieces that would indicate recent replacement.  

Flood Vehicles - Flood-damaged cars can be hard to spot.  Check the title to see if it has been stamped "submerged" or "flood car."  An obvious giveaway is a moldy swamp-like smell emanating from the seats and carpeting, but beware: a good doll-up and some new carpeting and interior components can mask most symptoms.  If you suspect a car has been flood-damaged and the title doesn't so indicate, look under the carpeting for sand, silt or salt.  Check the engine compartment, trunk, and inner doors for silt.  Flood cars are sometimes very hard to detect, even for professionals like me, but avoid them if at all possible.  I have yet to find a known flood car that didn't have electrical problems -- problems that can change on a daily basis.

Some Good Advice - Don't make a $10,000 mistake! A thorough mechanic's inspection is your best protection against buying a used car with costly, hidden problems.