First off I’ve never heard anybody call it a mark 3 Range Rover. Most techs I know call it a LM Range. The P38 is called an LP Range. It’s the 3rd and 4th letter in the Vin. Disco’s are LJ and LT.
Your going to want to check it for loose tie rod ends, the ball joints in the bottom of the knuckles in front. 2 on each side. If you have someone turn the wheel back and forth thru center you can see them moving when loose. Drive it at highway speed and get into some sweeping turns. That’s when you can feel those things if loose.
Jounce the suspension at parking lot speeds the same way you can make LR3 and LR4 lower control arms clack. When you do that on the LM you will make the rear most control arm bushing thud. Then the other lower arm has one of those ball joints on it. It makes a clack noise when you hit something like a curb going into a driveway. Expect to put air springs in the front struts if it hasn’t been done.
Look for coolant collecting on the lower edges of the radiator. You can see it by looking over the top of that plastic shield under the radiator. Also look for coolant under and in front of the right side of the supercharger. There’s some rubber heater hoses that run under there. Look at an exploded view of the cooling system and you should be able to figure out what I’m talking about.
I would want to check it for rear diff codes. The diff motor breaks internally and it costs close to a grand at a dealer.
I guess I would pull codes on the entire vehicle. If they cleared them recently I would be suspicious