I sliced up peeled potatoes and tossed them in oil and butter to cook them in a shallow aluminum tray. Then I covered them overnight and many of them turned black. If we bake them, are they okay to eat?

I am going to make a couple of assumptions, so correct me if this isn’t what happened…

1. The peeled potatoes were raw. When slicing they were exposed to air (which will cause them to quickly turn dark). One method to avoid this is to peel the potatoes, place in water covering the potatoes, remove and slice on a cutting board with a knife that is steel (some blades have iron in them and till will turn the potato dark). Then place back in water, drain and dry before cooking on a shallow aluminum tray.
2. The cooked potatoes were allowed to cool to room temperature, then removed from the tray and placed in a plastic container in the refrigerator for the next day. If the potatoes were left on the tray the potatoes could still turn color from the aluminum pan.

If the cooked potatoes were not left out overnight, unrefrigerated then they will be okay to eat. They will be pretty unattractive to the eater but will taste fine. If they were left out, then because of the dairy (butter) they would not be safe to eat.