Just had the battery unit on my MPB 2013 replaced under Applecare and while it was in they found a fault on the screen and replaced that too. All 10 days before Applecare expired. All FoC. They even held the part for a few days since I was busy and couldn't risk being without the machine for a couple of days (in the end the repair took 90 mins, but they always quote 2-5 days).
Would have cost over £600 without Applecare.
The issue was detected when I took it in for something wholly unrelated (which turned out to be a failing ext HD, not a Mac issue).