i'd give the sniff test to be safe, but i bet you anything they're fine, esp if they were put in the fridge well-covered. i've baked up potatoes and put them in the fridge and eaten then a few weeks later, no problem.
Apparently, my estimate is more conservative than most. However, if you do food-born illness search, you will find that cooked potatoes are on the 'high-risk' list. Their high moisture and low-acidity makes them spoil more quickly than plenty of animal-products so don't assume, being a plant (or simply not smelling bad) makes something safe to eat weeks later
I couldn't find a specific quote for potatoes, but California Poison control has this recommendation for all fruits and veggies ... [They] are good in the refrigerator for three to five days.
You can eat whatever you want, just passing on the info ... you crazy people
I would guess something like mashed potato or potato salad is higher-risk than large pieces of cooked potato or whole cooked potato, because it's mixed up and growth could begin way down in the middle where you can't detect it. With large pieces, bacterial growth is more likely to start on the surface where you can see/smell it before it's advanced very far.