Absolutely, if the IC socket is even slightly questionable, replace it. New PLCC sockets are not expensive and easy enough to source. If you don't have the tools and skillset to unsolder it, take it to someone who does, else you're likely to cause more damage to the plated through holes and PCB tracks. It only takes a few minutes with the correct tools.
Even if you manage a 'repair' on the damaged socket, you'll still have the other intermittent issues that will likely cause ongoing problems long term.
Be sure to clean the leads on the IC as well; isopropyl alcohol on a soft cloth. Don't bend the leads as they're easily damaged. And avoid contaminating the cleaned leads with finger grease after you've cleaned them.
