I am not so sure there should be 1 mm play. I have no play in mine and haven't for 60 000 kms. Suggest this is adjusted out.
Balancing machines need calibrating. Only go to the shops that deal with high end cars as they will have been made aware of this and chances are they have proper machines and trained technicians. This is very important and often overlooked. Also, balance weights do have a habit of comming off especially the inside ones if they rub at all on other suspension or brake parts. This is a very common problem, especially if thicker "stick on" weights are used instead of longer thinner ones. As much as I don't like it, I have found that the stick on weights tend not to be as accurate as clip on ones, even if they do tend to prevent damaging the coating on the wheels.
Pull to the left seems common on Mercs but is solvable. MB have a tech note on this and suggest if it is a problem after the car has been set up correctly, then increase the castor on the left to create up to a degree of difference between left and right. There is also an adjustment to the camber between left and right sides that will make a difference. Check Wheels In Motion postings on this........
Regards to all, W.