The fault is not within the episode, as TOS on television never precisely pinned down the century. The blame goes to TWOK (Star Trek II seems to be superceded by the Abramsverse), where we finally are told "In the 23rd century..."
Khan also says, "On Earth, 200 years ago..." which contradicts that title card.
And there are a couple of items in TOS:
- Col. Felini told Kirk, "I'm going to lock you up for 200 years," which Kirk said was just about right. ("Tomorrow is Yesterday")
- Scotty said "Lincoln died three centuries ago" ("The Savage Curtain")
Both of those references put Star Trek
200 years after the time it was filmed. I don't like that either; I say it was casual talk not to be taken as exactly right. I say 300 years like the official Chronology does.