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Yup, something got bent/broken/out of alignment when you dropped it. The scale may or may not be worth trying to salvage. (I'd love to take an eyeball look at it.)
As to the damping question, that isn't an iron or steel plate that rides between the magnets. I can't imagine what that would do for accuracy! (Actually, I can and it isn't good.) The plate must be non-ferrous to be an effective damping system, usually a copper or lead alloy is used. As the arm (and therefore the plate) slows down as it reaches equilibrium, the magnetic damping effect (eddy currents in the plate) falls to practically zero.
[And on the definition of dampening vs damping: Dampening is an acceptable word to match the definition of reducing the amplitude of oscillations. To dampen does mean, primarily, to moisten or wet as with water. Secondarily, it means to reduce vibrations.]
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