How can I know whether a potato is too old?
It likely depends on what 'turning bad' means ...

If you have a couple in the bag starting to sprout, but the rest haven't, you can roast or bake the ones that haven't sprouted, let them cool, then store then in the fridge so you can pull them out to use them in something later in the week.  (eg. home fries, patatas bravas or a hash).

For those that have started to sprout, but are still firm, you can cut away the sprouted bits (this time of year, you might even be able to plant them), peel them, and then boil them and turn 'em into mashed potatoes (which you can then vary for the next couple of days ... you can mash 'em with other stuff to make a sort of potato salad; you can add cooked greens to make colcannon or bubble and squeek; you can use as a topping for a cottage pie (the technically correct term for shepherds pie when you're not using mutton or lamb)

Some of these freeze well ... I've made up cottage pies and frozen 'em in oven-proof containers; you could likely do the same with just mashed potatoes -- I see 'em for sale in the grocery store all the time.

If you're looking for something to cook that just uses a lot of potatoes (in a non-whole state, in case you need to cut away parts) ... potato salad, potato bread, potato curry, latkes, potato soup, tortilla de patatas ... the list goes on. 

... and if they're soft and squishy, or oozing liquid ... pitch them.  They're rotting, and not worth getting sick over.