Black spots on potatoes are usually caused by a condition known as "black spot bruise" or "internal black spot," which occurs when potatoes are handled roughly or dropped, causing cells under the skin to break and turn dark. Stopping irrigation is important for proper skin set and storage quality but letting the soil get too dry for several weeks before digging makes bruising and black spot symptoms more likely. It can be a balancing act: stopping irrigation to help skin set but not allowing soil (and therefore tubers) to dry too much if you want to minimize blemishes. When irrigation is stopped early, potato tubers slowly lose turgor (firmness) and become slightly dehydrated. Dehydrated or less-hydrated tubers are more easily bruised during harvest, even the gentle pressure from digging by hand can damage their cells, and this shows up as black, brown, or grey blemishes just under the skin.

For management:

Rotate your crop to a new location in your garden and do not plant potatoes in the former location for at least three years out of potatoes.

• Plant only certified disease free seed potatoes.
• Crop rotation for longer than three years may help reduce the inoculum level in the soil.
• Carefully manage water and fertilization to avoid crop stress.
• Maintain balanced fertilizer (adequate potassium, not excessive nitrogen)
• Harvest tubers as soon as possible after vine kill.
• Dig gently, especially with sensitive, red-skinned, and smooth skin varieties.

This problem can also be caused by certain fungal diseases such as black spots, but most commonly it results from physical damage. To prevent black spots, handle potatoes gently during harvest and storage, avoid dropping them, and store them in a cool, dark, well-ventilated place.

Black spot is a disease that affects roots, stems and tubers and is named after the small black, dot-like structures (sclerotia) that form on the surface of infected stems, stolons, and tubers. Black dot first appears in mid- to late season as a yellowing and wilting of plants. These symptoms are easily confused with Verticillium Wilt or early dying associated with bacterial soft rot. Wilting caused by black dot develops rapidly, in contrast to Verticillium wilt.

Black spot can be managed by planting certified seed tubers, maintain adequate levels of nutrients, and avoid overirrigation. When fields become infested, they rotate to nonhost crops such as grains for at least 3 years, and control potato volunteers and potato family weeds in the rotation crops. No potato cultivars are resistant, but early season cultivars may escape some damage in infested fields, and the tubers of russet cultivars are less severely affected than tubers of thinner-skinned cultivars.

I have included a resource for more management options, here is the link as well : Potato (Solanum tuberosum)-Black Dot

Potatoes with black spots are safe to eat if you cut away the affected areas and the rest of the tuber is firm and free of mold or a rotten smell. If the potato is soft, has an off odor, or shows signs of extensive rot, it is best to discard it.

Thank you for your question and have a great gardening season.