These really are decent cars if you remember to keep up with the maintenance. I have 160,000 miles on a 93 SL2, so it's a little different than yours having the dual overhead cam motor and an automatic transmission.
Mine never had any trouble until 147,000 miles, which is when the alternator went.
The ECTS is the engine coolant temp sensor. This is very cheap to replace. I didn't know mine went bad, and the car started getting poor gas mileage because the car was running rich and I didn't know. There really isn't any other indication. Eventually this damaged the catalytic converter on it. So, just replace it before this happens. It only costs about $8-$10 at an auto parts store and could save you some trouble.
I have no idea what a TAM is.
At 156,000 miles, you probably should have the radiator hoses & coolant replaced if that has never been done. Also make sure the serpentine belt is in good shape. If it has cracks or tears running parallel to the belt (as opposed to across it) you need to put a new one on there. Sometimes you replace the belt and yet you still have squealing from the belt, or the alternator can't keep the headlights fully bright. In this case it could be the belt tensioner going bad. It costs about $100 (for the part) to replace.
Make sure the spark plug wires are changed if they are still original.
One thing to listen for when test driving is if you hear a whirring sound from the wheels when you drive. You might need wheel bearings if you hear this noise. They are fairly expensive to replace ($100 for the part alone). One of mine went bad after hitting a curb.
This hasn't happened to me, but I have heard if you get misfiring in the engine, you should add a bottle of fuel injector cleaner into the gas tank. Apparently the fuel injectors get clogged sometimes & cause this.
Always check the oil and keep it above the ADD line on the dipstick. As someone else said it will probably burn some oil at this mileage. Keep the oil changed every 3000 miles, and don't let the engine overheat (it has an aluminum block and head)- and you should stay out of trouble. On automatic transmission cars you should change the fluid every 30,000 miles. You shouldn't have any problem getting to 200,000 miles on one of these.
The front end shimmy sounds like a tire out of balance or a ball joint or tie rod needing replacement.