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Spotted, dark colors on leaves are an indication of serious problems with your plant. Plant leaves turn black for a number of reasons, including environmental factors and bacterial infections. In some cases the plant is salvageable. However, most of the problems that cause black leaves in plants are irreversible. In every case, prevention is the best way to deal with the disease and dehydration that are common factors in blackened leaves.
Black leaf tips are more likely to be caused by underwatering than overwatering. (Yellowing of leaves is more likely with overwatering.) However, the black tips are more likely an indication of low humidity than underwatering. If possible, try grouping the peace lily with other houseplants to raise the humidity in the area around the plants. The blackened leaf tips could also be due to excess salts in the soil, either from too much fertilizer or fluoride/chlorine in the water.