I purchased a red onion yesterday, sliced it open and noticed that it felt slimy on the red skin of one of the exposed inner layers. I've never noticed that before. Is that normal, or has the onion gone bad?
Some slime building is normal in onions and related vegetables, see this question. It is less pronounced in bulbs than in leaves, but it can occur. If your onion bulb is solid, there is no problem with it.
Sometimes you can have spoiled slimy onion bulbs. In this case, spoilage microorganisms eat away the firm cell structure of the onion and leave you with slimy mush. You can recognize this easily: if it has happened, the onion has a patch which feels really soft, and is much slimier than the rest. It is often discolored, and can also smell strange. It looks and feels very different from a healthy onion with a slight slime layer. I can't be 100% sure as I haven't seen your onion, but from your description, it sounds like it wasn't the case this time.