Listen for any knocking/rattling noises from the engine when it's warm and it's idling,the dephaser pulleys are a common problem on these and are expensive to replace.Even if the dephaser is quiet,check the cambelt history (due every 5 years/72k),the belts do break if neglected.
If it's a manual then make sure the clutch and gearbox are smooth and gearchanges are easy.Clutch hydraulics are another known weak point,gearboxes aren't exactly strong either.If it's automatic,then don't go anywhere near it.......no,really don't!.
Make sure everything electric works,pay particular attention to the dashboard readout as they can give trouble.Make sure the check read out (if fitted,mines got one so I guess all Espaces have one) goes through all it's checks and comes up with 'OK' after initial start up.Make sure the remote for the radio/CD is present and working,make sure the radio and CD multichanger all work as they should.Check the aircon and heating all work as they should.Check the remote locking,ideally it should have two working key fobs.
Check all of the rear seats and seat belts for damage,also check the centre row centre seat has it's removable lap belt.The interiors can get abused and don't tend to hide it too well,although ours has been pretty good so far considering the amount of abuse it gets!.
Check all the panels for damage,the bonnet is steel but all the outer skins on the doors and front and rear wings are composite plastic/polyester/glass fibre type material which cracks when hit (it won't dent as such,ours is sporting a rather fetching hole in the nearside rear door where my dear wife had an arguement with a wall that apparently drove into her.....
).It's difficult/impossible to repair the panels any sense and replacement can be expensive although there are plenty of Espace 3's being broken out there to be able to find a decent second repacement panel/door.
If you buy carefully then the Espace is a good car,I must admit I was very reluctant to have one but after 18 months of ownership the bus has grown on me.They definitely have their 'quirks',but by and large ours has been good and is comfortable and pleasant to drive (not fast by any means,and the handling is 'soft' to say the least,but it does what it's supposed to very well).I'll be honest and say that before I owned one I would never have recommended anyone I know to buy one,but now my opinion has changed slightly.
If you buy a bad one though it will be a nightmare.....a very expensive and infuriating nightmare.