The black spots are typical of a fungus/virus/bacteria infection brought on by stress from overwatering or poor sanitation at the growers. This looks like the very common Cylindrocladium spathiphylli for which the symptoms are described as "dime size circular brown necrotic lesions form surrounded by yellow halos".
Remediation for growers is destroying the infected stock and treatment of the growing area with a fungicide not normally available to homeowners.
Good news is that you can treat this condition yourself:
- move to a higher light area
- do not allow the plant to sit in water
- change the plant to a pot in a pot system and add a wicking system as described here
Most healthy plants can outgrow infections if they given better conditions.