The potential deal-breakers are:
Lack of service records. Your car needs routine maintenance to stay in good condition, and you should make sure the used car you buy got it too. Ask the seller, even if it's a dealer, for all service records. If you can't get these, you have no way of knowing whether the car has been properly maintained. Also look for a windshield sticker indicating when the next oil change should occur. If you cannot find it, or it shows that the car's past due for a change, ask the seller why.
Accidents and vehicle history issues. You should obtain a vehicle history of any used car you plan to buy. The dealer should be able to provide one, or you can locate it yourself using the car's VIN (vehicle identification number) online at AutoCheck. The report will tell you if the car has past damage to the body or frame, has been involved in any accidents, has title problems, or has had its odometer rolled back. Any of these should torpedo the sale. AutoCheck charges $19.99 for a single report or $29.99 for 60 days of unlimited reports.
Mechanical problems. A used car may have mechanical problems that don't show up as puddles under the car body. That's why a pre-purchase inspection (PPI) is essential. Performed by a neutral third party such as a certified mechanic or auto technician, a PPI provides a detailed report on the car's structural, mechanical and cosmetic condition. It can reveal maintenance problems and damage lurking beneath the surface. The inspector should use a paint meter gauge to detect any repainted body panels - usually a sign that a car has been involved in an accident that was not reported to the insurance company - and put the car on a lift to check thee undercarriage. You should use an inspector of your own choosing rather than rely on the seller's recommendation.
While a PPI runs anywhere from $100 to $200, causing many buyers to skip it, it is worth the expense. If it catches problems that aren't deal-breakers, you can use the knowledge to obtain a lower price for the car.
A problem title. The vehicle report will show any problem titles in the car's history. Avoid titles that show severe damage from hail, fire or flood; shun salvage titles, which indicate that the car was at some time in the past declared a total loss, and junk titles, which declare that the car is not safe to use and cannot be titled again in the issuing state.
A fraudulent title. Even a clean title may not really be clean. Criminals can create fraudulent titles and use them to legally register and sell stolen cars. Buy one of these, and you may end up losing the car you thought you owned, because it's not legally yours.
The first step in checking for title fraud is to run the title past the DMV. This may involve a modest fee and a trip to the nearest DMV office. At the very least, the VIN on the car should match the VIN on the title, and the seller's name should be the same as the name on the title. The check will also turn up any outstanding liens on the car, which mean that the owner is still making payments and does not own the car outright. If you're buying from a private seller, liens could complicate the deal.
Also check for subtler signs of fraud, such as an obscured VIN or other signs of tampering on the car or title, or title documents that do not appear crisp or are not printed on special watermarked paper. If you can, you might want to compare the title of the car you're considering to an original title for another car in the same state.
While these steps add time, cost and complexity to the process of buying a used car, they will save you money, embarrassement, or worse down the road. You can always walk away from a deal before you make it; cleaning up messes afterwards is far more troublesome.