Brakes, 135,000 and again, 150,000. Front calipers tend to seize and wear out pads prematurely. My back brakes have always been noisy, but no mechanic has ever really nailed what's wrong.
Alternator, 155,000 and again, 175,000. Rebuilts are around 75 USD, but quality varies.
Rack and pinion. Several symptoms of trouble since I've owned the car, but none bad enough to warranty replacement.
Seat springs have been worn out since I got the car; seats offer little enough support even in good condition. Upholstery is of poor quality, does not clean well, fades badly in sunlight.
Transmission. Hunts irritatingly btw. 3rd and 4th gears, lugging engine and reducing performance to nil btw. 40-55 mph. Trans shop says this is normal. Using low-3 helps performance and driveability with minimal reduction in fuel efficiency.
Front struts, 155,000.
Front ball joints, starting to get loose now and will need replacement within 5000 miles.
Springs. All four corners of car are riding too low and have been for a long time.
Air conditioner. Compressor end seal leaks. DIY conversion to R134a and yearly refill is cheaper than a real repair.
Door panels, armrests: Coming apart and falling off since I bought the car. No GM car was very good in this department in late 80s.
Paint: Clear coat comes off, esp. on roof.
Rust: I have seen some other LeSabres rust badly where the subframe meets the unibody behind front tires. My southern car is just now starting to get scaly rust there. Seems to rust outside-in, so you can Rust-Oleum this area and keep it together for a while. Surface rust common on rear quarters in front of wheels. Also rusted badly on front inner fenders.
Power windows: Front motors are nearly dead, but will work with a boost. This way since ~ 150,000.
Radiator: Minor leak started ~145,000, fixed with Bar's Leaks. One tank burst at 160,000.
Water Pump: Replaced at 135,000 due to leak. Replaced at 165,000 due to bearing failure and lockup which broke serpentine belt.
Taillights: one socket needed to be rewired up to the dash due to unknown short.
Rear main seal: leak is small, but would be expensive to fix if it got bigger. Since 135,000 at least.
Mass Airflow sensor: 160,000. Try to get a good used one if you can, as these are *way* overpriced in stores.