1) Look for fluid leaks. These engines don't really leak oil, but the plastic transmission pans & electrical connector on the passenger side of the transmission will leak ATF.
2) Run the suspension down to Access Mode, to Offroad Mode and then back down to Standard. The rear usually raises before the front, but look for signs of uneven lifting (i.e. side to side). You want to make sure the vehicle lifts quickly, goes full range of motion and you don't get any warning signs. (i.e. Vehicle Raising Slowly). Another reason for this is to check for leaks. When small cracks develop, sometimes they can seal when squeezed up against the strut body. By raising/lowering, you flex the rubber in the air spring and can sometimes expose air leaks in the spring.
3) Check the air filters & cabin filters. Too many people think "service" is just oil changes. If the filters are disgusting, it sets the tone for the condition of the rest of the car. Don't forget to pop the oil cap too. The underside of the cap is usually how the rest of the inside of the engine looks.
4) If you have a pocket code reader, bring it. We do more Catalytic Converters on Land Rovers than any other brand we service. P0420 & P0430 are common (at least for us).
5)I'm sure there is more, just can't think of anything else at the moment. The pre-2010 S/C engines are pretty good. 2010+ is a different story. Just look for the same things as you would for your LR3, many items are the same (i.e. control arms are different but still suffer similar bushing issues)