Refrigerating leftover cooked potato
Refrigerating cooked potatoes is perfectly safe.  The myriad of frozen and refrigerated potato products on the market demonstrate this, as do the experiences of millions of home cooks.

In fact, it is raw potatoes that should not be refrigerated, not because of safety concerns, but because they will convert starches to sugars and taste oddly sweet.  The ideal storage temperature is slightly higher, 45-50 F.