Yes, cooked potatoes are safe to eat after being refrigerated, as long as they were handled properly.

A few important things:

• Refrigerate them within about 2 hours of cooking
• Store them in a sealed container
• Eat within about 3–5 days
• Reheat thoroughly if serving hot

Signs to toss them:

• Sour smell
• Slimy texture
• Mold
• Odd taste

Cold potato salad, roasted potatoes, mashed potatoes, and baked potatoes are all generally fine refrigerated when stored correctly.