Check for correct engine running, starting from cold should be prompt, and it should idle smoothly straight away. The engine should pull strongly straight after starting, and should continue to do so, even when hot.
Make sure it's not been run on a budget too, and should ideally have full dealer history, not that that is proof of it being well maintained, as I've undone loads of main dealer bodges over the years.
Check the whole vehicle carefully, making sure paint and interior are not showing signs of wear or neglect. Also make sure everything works as it should, as it's expensive to replace failed electronic units, and many need to be configured to the vehicle.
Check underneath for rust on the outer sills, and the front are rear subframes have no more than surface corrosion.
Importantly you want to make sure it's had all the drive line fluids replaced, long before LR suggested. The fluids in the Haldex, rear diff, PTU and gearbox are all supposed to be done at 150k or 10 years, but this is way way to long, as these components won't make 150k without fresh fluids. The Haldex is the same as that used in VW/Audi vehicles, where have a 3 years/ 40k change interval, so best its done at those intervals.
The diff is an interesting issue, which affects ALL years of Freelander 2, and the early RR Evoque too. Diff failure can occur from anywhere between 20,000 and 100,000 miles. It's completely random, so is more than likely down to the individual diff that is fitted.
There is normally just 1 bearing that fails (unless there's no oil in the diff)(you can read how I know!!), but pretty much all rear diffs suffer the same failure. To me it's due to a combination of over pre-loaded pinion bearings, and poor lubrication of this design of diff. The former, is accelerated by the latter.
Listen out for a bearing type noise from the rear on a test drive, although mine wasn't actually that noisy before it seized solid, as it had no oil in it at all.
Oh and don't over pay for bad condition, or low spec models, as there's always plenty for sale.