I strongly agree with Mike and rovertech,but in case you are not allowed to take the car to another shop for a "second opinion" here are some basic pinpoints in no specific order except for the first one

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1.Take a trip to the lot wearing a pair of old jeans and a "not so good condition" shirt...reason? you will be reaching underneath the truck looking for leaks or other irregularities.
2.While the engine at idle,look for leaks underneath and viewing the vehicle from the front.Also look for leaks in the engine compartment,if the vehicle was "just washed and detailed" drive it up to a dry spot.
3.When you shut off the engine go to the front of the vehicle and see if you smell coolant.If you do,this is a common happening on Discoverys,which could be a leaking radiator,lines,hoses,or worse than that,head and /or intake manifold gaskets.All this is fixable,but could be expensive if you don't do it by your own or through an independent reliable shop.Believe me,I just went through a refurbishing of the upper part of the engine by my local LR dealer on my Disco with new gaskets,head bolts,idler pulley,exhaust gaskets,etc replaced...the charge? a bit over $2,000 bucks,as I don't have a local independent and RELIABLE repair shop around where I live.As I said in another thread:If you can't find a reputable shop around your area,go to the dealer,as they might be expensive,but will stand behind their work and warranty,rather than jumping from shop to shop misdiagnosing the problem and probably spending more money than if taken originally to the dealer.
4.Look underneath the vehicle behind the back wheels and look for grease leaks around the brake rotor area,also look for both front and back differential leaks.
5.Discoveries have almost a dash indicator light per system,so look for abnormalities,particularly the amber "service engine soon",abs,and srs/airbag lights.
6.Check if the truck misses at idle,could be a problem in the MAF sensor,O2 sensors,or just a dirty air cleaner in need of replacement.All these parts could be bought through any parts supplier online and could be replaced in your garage,driveway,or backyard;nothing big though;but always pretending that it IS a big issue in front of the salesman,so you can see if he or she lowers the price a bit for that reason

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Parts suppliers are available online with better and really competitive prices than dealers,so if you don't find anything compromising with this truck you placed a deposit on,I would say go for it!
I think that you could have a general idea of what to look for now.also welcome to the LR world!!! :drink1:
Carlos