What are the signs that an extension cord is dying and should be replaced?

Heat at the plug or connector and intermittent power (flickering lights, tools cutting out) are the two main signs. Heat means a loose or corroded connection inside that can melt insulation or start a fire. Intermittent power usually means a broken or shorting wire, often at the bend point. Both are “replace now” signals — don’t wait for it to get hot to the touch.