When you have an old piano (40-60 years old), and it’s a spinet, then most likely there are clicking sounds when you play the keys.  Below you’ll find some pictures of the reason why these pianos are clicky.  On the back of the keys there are little rubber grommets (some are square, others are round) that assist in regulating the spinet action.  Find the rubber just below the red felt punching:

Over time these rubber grommets become hard and brittle and cause an loud clicking noise as heard in this video:

Then here is a video of what it sounds like after the installation of the new Rubber Donut Grommets: