Slimy whey in store-bought yoghurt
It's probably thickeners, such as carrageenan or xanthan gum, which are thickening/sliming up the whey. Draining off the whey or stirring it back in should be fine. A brand which doesn't have added thickeners (look for "strained" or "Greek-style" yogurt, then read the ingredients) won't do this.

I've had yogurt go off many times, and slimy whey isn't how yogurt goes off. The whey is nowhere near as tempting to microorganisms as the yogurt solids, so you'll see mold (or whatever) on the solids first, not the whey.