Hello Julian,
I have a 73 Twin Cam Special, which I restored in 2000. It was a 'vision' of mine since 1972 so I took the plunge in 1997 and bought a complete but needed complete restoration TCS in black with gold stripes.
What to look for? Well, since it seems it is a california car, then the frame should be in good order. They are sheet metal and weigh in at only 80 pounds. The original paint wasn't done too well, and if water has leaked in, you may have a problem around the top of the back bone. They used a horse hair matt between the body and frame and if that soaks with water it can create rust. Other spots are the front of the tee around the bottom areas. The Specials don't have the cracking problems as the earlier versions between the tee and the backbone. Look for accident damage too. The frames are very light, and do okay with normal road shock, but accidents can have detrimental effects and are difficult to straighten. The factory recommended frame replacements for any serious shunt.
The rear axles are a problem area also, as mentioned previously. They are an adaptation from the Hillman Imp. The problem is that they were made originally of a lower grade steel and the splines would wear. Also, the bearing spacers would compress (again, lower grade steel) causing the ball bearings to be put into lateral stress, causing premature failure. The axle carriers are aluminum, and the bearing fit can be fatigued out if not put together right. All the bits are available, and there are some better than original upgrades you can do to improve their reliability. The TC Specials have the better carriers with larger bearings.
The transaxles are Renault, and are very nice. My car has 125k on it now, with the original 5 speed gears and all. They do have trouble with weeping around the axle output seals, this is normal and not detrimental. The rear may also leak a bit, where the shift mechanism enters but seals and bearings are available. The shift linkage can be trouble, since it is made of tubing with sealed needle bearing u-joints which get water in them, and freeze up if let sit. You can upgrade to a cable shifter, go to a side shifter, or replace the bearings. I went to a side shifter, and an early linkage so it is more positive. Others have had good luck with just replacement of the u-joints.
The front suspension is similar to a Spitfire, and uses some of the same components. Shocks are coil over and you can get adjustable height and damping along with stiffer springs for a very nice handling car.
The twincam motors are sweet. Though they can be expensive to rebuild. I STRONGLY recommend if you have to rebuild it, send the cylinder head to a shop experienced in these heads. They have short valve guides which results in more frequent head restoration needs. I had mine done by a local guy who had done them before, and though it took 6 months to finish, he did a good job. The tricky bits are the guide removal and reinstallation, the seats and grinding to proper valve height, and particularly the cam tappets as the sleeves may need replacing if they wear more than .002 oversize. The lower end of the motor is pretty stout and can be rebuilt easily. Overbore max is .040 though you can sleeved if it cannot be bored further. Be aware though, this is not your chevy small block, and it needs TLC to get it assembled so it doesn't leak too badly. If you are serious, and want to take on a twink, get Miles Wilkins book on the motor, a must have. Ask how many miles on the last rebuild, and if over 30k, consider at least a head rework is in order which will require valves, guides and possibly tappets.
The brakes are dual power assist, with drums rear, and disks front. Interesting in such a light car. Servo rebuilders are out there (one in San Jose) or you can replace with new Lockeed units. Some have removed them and done okay with just new pads that have a higher friction factor and tolerate the stiffer pedal.
The body will have stress cracks, and they are repairable by several methods but will require a repaint, obviously. The doors may sag, but that is due to the fiber washers holding the door pin in place have sliped. Since the pins and bushings are steel, they often rust and can be difficult to remove.
I really love my Europa, its the best handling car I've ever driven. I take it on track days and on the back twisty roads and have a blast. An E ticket ride and you don't have to exceed the speed limit (or not much anyways). But it isn't a highway cruiser as its noisey and not too roomy. If you work at it I'm sure you can make it quieter. The pedals are close together, and you'll need narrow shoes to negotiate the brake and throttle.
The Europa List on Yahoo is a very active set of enthusiasts. You'll have to join if you purchase the Europa. They have a web site managed by Jerry Johnson, which is great and you can search all the archives very easily.
Good luck,