"This warranty does not apply to scratches, stains, discoloration or other damage to the unit which (does or do) not impair the functional utility of the item".
Hi Katie
It's usual in constructions like this, where there is a list of items, for the relative clause to modify the nearest noun or noun phrase. In this case it's the noun phrase "other damage to the unit" whose head word is the non-count noun "damage". Non-count nouns take singular verb agreement, so singular "does" is correct.