Microwave the potatoes before putting them in the oven for about 7 minutes(start with 5 minutes, add 30 seconds every time till done), covered with a little water (very little, couple of spoons full)(potatoes whole or sliced)
Make sure you're not using a 'heavy' oven dish, glass ones can taka a long time to heat up. Place the oven dish into the oven while heating and add a drop of oil. When you put in the potatoes you should hear a little 'hiss' indicating the termperature is right.
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.
Best Answer
Great question easy fix as I had the same issue. Set aside or add a couple extra chunks or potatoes that is just for testing. When you test a chunk toss it, the test potatoe will be representative of how the other potatoes are cooking, it allows you to puncture without compromising the rest of the batch.