The only way to check the U-joints in an Alfa driveshaft is to remove the shaft from the car. The U-joint first loose their grease and get tight. Only after a considerable time do the become loose. This is when the inner shaft essentially wears out. Usually the vibration will start before the U-joints have worn to a point where you can feel the slop. With the drive shaft out of the car move the U-joint. It should flop around with little or no resistance. If it is hard to move, it is most likely bad and must be replaced.
The technique for replacing the U-joint is more difficult that the beat-it-with-a-hammer-until-it-is-out American car method. The Alfa drive shaft is somewhat fragile and you can easily bend the shaft by pounding on it. I do mine in a press so as not to bend any of the components.
The proper technique utilizes a press and the cups are pressed outward only. This, however, requires quite a lot of fixtures, which the average mechanic does not have. I have built these fixtures after watching an expert do the job. It is amazing how easy this job can be done with the right tools. Check with your local drive shaft repair shop to see what they charge to do the job. You may find that for $30-$50 it is better to let someone else do the job. At the same time, they can check the shaft to see if it is bent, which is a very common problem.
Inspect the center bearing and the rubber between the bearing and the center housing for tears. Also inspect the rubber donut for cracks or missing chunks. Always be sure to mark everything so you know how it goes together.
Another way to remove old u-joints is with a cutting torch. Just slice up the u-joint so the cups can be pressed inward. Properly done the yoke does not get hot at all. Without first cutting away the main body you have to first push the cup in to get the opposite side out and then reverse the process to remove the other cup. This is commonly done by the hammer and socket method which often bends the yoke.
Before trying to balance a shaft in the car try rotating the way the shaft connects to the rear end and to the short shaft. Often the drive shaft is removed by someone who does not mark the way it came apart and the balance is off. When the car is in the air with the shaft removed, run the engine to see if there is any vibration from the engine or the short shaft.
When the u-joint is properly installed it will move very easily and have no drag or binding. If there is any binding the u-joint will not last very long.