"iTunes can’t verify the identity of the server ..." after a Security Update in Mavericks or upgrade to El Capitan
The reason:

After installing Security Update 2015-004, multiple users found that they couldn't browse to any website using the root certificate "VeriSign Class 3 Public Primary Certification Authority - G5" without a security warning ("invalid certificate"). 
2015-004 updated the list of trusted root CAs, and for a reason I'm still unclear about, many of us have an identical entry in our Login Keychain. The certificate name is the same, but the serial number is wrong. The conflict causes the problem.

The solution:

Open Keychain, and look up your Login Certificates. Export any Verisign certificates (as a backup), and then delete them. Restart your browser.

I had the same issue and asked it in https://security.stackexchange.com/questions/85830/why-is-symantec-verisign-ca-appearing-as-an-invalid-authority .

You can see a full discussion in https://discussions.apple.com/thread/6984765