Like donbryce said, play should be set to 0.01 - 0.02 mm (0.0004 - 0.0008"). I wouldn't get too excited if it was set to 0.0010" -- after all, it's better than any shadetree method, plus the spec for checking the play during inspection is 0.01 - 0.05 mm (0.0004 - 0.0020").

Though your tires may look fine, the tread may be delaminating on the inside. This would cause tremendous shaking.

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95 E320 Cabriolet, 169K