Hi
All S-type R engines are great, all 4.2 had no issues with nikasil bores or chains or tensioner, that was solely on the 4.0l, when the 4.2 came these were all resolved and as all S-type R are 4.2 there fine.
main issues with the engine is the Valley pipe, a coolant hose buried in the V, that balloons with the heat and burst, £20 for the hose about £500 to £800 for the labour
check for any rattling as supercharger coupling can fail, causing a noisy supercharger, generally if abused
engine and gearbox should be silky smooth and should have plenty of go
as for all s-type check Sills, Sills, Sills, they can rot terrible here and still pass a mot, it hidden by a plastic cover remove to see, also if sills are bad usually rear arches will have bubbles of rust leading to sills.
there's a lot of bushes on the S-type and if the cars been abused, then they can eat bushes, like I said it should drive silky smooth, no knocking or rattling
if its pre 2005 it will have Brembo brakes all round, make sure they work ok, also check the EPB works ok, try it a few times as they can be trouble some, brembo's had a seperate caliper at the rear solely for handbrake, later cars went more to cost effecting brakes and in my opinion not as good as the brembo's, brembo's had 2x 4pot calipers at the front and 2x 4pot caliper at the rear and a seperate parking brake caliper at the rear, later cars had, 2x 1pot calipers front, 2x 1pot caliper rear, with integral parking brake.
make sure the heating and aircon works, trouble some DCCV can cause problems and be expensive to fix
lift the boot mat, there prone to leaking water inside the boot from above the rear lights
check both keys work, all the functions, just because it comes with 2 keys don't assume both work, can be expensive to reprogram and replace
the STR's have HID headlights, there self leveling, every time you switch the ignition on they do a dance, they go all the way up, then all the way down and then level, if they dont, either a sensor has failed, or adjusters inside the headlight have broke, they can be replaced, but very time consuming, bumper has to come off to remove headlights and any faults need jaguar IDS/SDD software to be plugged in to clear
brake pipes also corrode, right next to the fuel tank, there a mare to do, fuel tank has to be dropped
a good one will come with lots of history and receipts/bills, service history is great, a must really
see what options it has, mine came fully loaded, 2003, 2004 came as a R plus and had more items a standard, can make a difference to value, features like phone, bluetooth, Audio connectivity Module, Jaguar voice, adaptive cruise, Jaguar tracker, 16 way adjustable memory seats, adjustable pedals, rear entertainment screens, Alpine premium sound system
apart from that there brill, I bought a low mileage one , with full jaguar service history, its gone up over 2.5k in value in just 2 years and is serious fun, never had any issues with mine, but is been well looked after
cheers
Joe