Regarding the recalls; Get the VIN and enter that number at
https://www.nhtsa.gov/recalls to check for any unrepaired recalls. As for the overall condition of the '11 QX56 you are looking at, ask for a CARFAX Vehicle History Report and any service maintenance documentation that may exist. These two things are the most basic forms of vehicle history one could ask for and any reputable independent or franchise dealer should provide, even without asking for it. Adhering to preventative maintenance schedules are critical to the life expectancy of any vehicle. Going above and beyond the manufacturer's recommended scheduled maintenance requirements will assure an even longer lifespan. This brings me to my biggest pet peeve. For the '11 QX56 and many other vehicles produced in the past 15 years or so, their is no recommended maintenance for the automatic transmission. It is a sealed system. The ATF that was poured into the transmission when the vehicle was built was expected to last the life of the vehicle. This "life" is guarantied by the original power train warranty but that 6yr/70K mile warranty is long past expiration. There is nothing magical about the ATF that was added when the vehicle was built. The transmission itself was built with higher reliability, able to perform longer without wearing out even though the ATF has degraded over this guarantied lifespan. I can guaranty you now, that the ATF in that '11 QX56 is long overdue for a change, if it has never been changed, and the transmission is already starting to wear out due to the lack of adequate lubrication. If you do find that this QX56 drives well and it does not seem like the transmission is slipping under load, like quick accelerations and driving uphill, and you do decide to purchase it, I recommended you get the transmission ATF changed right away. This transmission should last at least another 125K miles but not if you fail to change the ATF at least every 50K miles. Typically, vehicles without "maintenance free" transmissions have recommended scheduled ATF changes every 35K miles.