Hi & welcome to the forum.
Have a look at the sills from inside the car if you can, by lifting the carpet. If the inner sills are rusty you will see this easily. Outside the car look at the underneath of the sill (there should be some drain holes you can shine a torch into), & the joint with the bottom of the rear wheel arch - this is prone to rust out where the bottom of the rear wing meets the sill. At the front of the sill it kind of tucks in behind the bottom edge of the front wing so look for signs of repair or welding there.
If you can lift the carpet then you can check the trailing arms - it's not usually the arms that crack, it is the locating points on the chassis at the rear of the floor. Look behind the seats & see if the floor is sound. If there is rust damage or cracks then the trailing arms mounts may be in need of repair. Have a look from underneath as well of course.
And while you have the carpet up look at the front floors too. Any rust should be obvious.
In the engine bay check the turrets & inner wings. Check the seam where the inner wing joins the bulkhead/firewall. In the boot look at the spare wheel well, & the inner arches.
Apart from obvious oil leaks in the engine bay, check the coolant in the header tank/expansion bottle for signs of oil mixed in with the coolant. Can you get a test drive? Best way to check for overheating problems is to drive the car a good distance (20 miles?) & watch the temp gauge - the needle should sit between 1/3 & 1/2. If it goes over half way then could be problems with water pump or head gasket - or both!).
Let us know how you get on[:)]
Tony
<font size="1">1981 2L FHC Cavalry Blue
1980 3.5L V8 DHC Jaguar Regency Red</font id="size1">