Add to the list of "two hundred years" references Sulu's comment about the handgun he found in Shore Leave - an antiquie which hadn't been manufactured for a couple of centuries, according to him.
The Smith & Wesson Model 10 is still in production (four inch barrel only), at what point in time will it be no longer manufactured? If they are produced passed the time period of the third world war, then Sulu's estimate is fine.
Also, Sulu statement of "hasn't been one like this made in a couple of centuries," could be somewhat vague. Today someone could make the general conversation statement that the American Civil War started " a couple of centuries ago," and they would not be politely called on the 49 year inaccuracy. General conversation.
And in Space Seed, Kirk's response of "two centuries we estimate," might have been partially base on his earlier belief that they were dealing with a DY-500 spacecraft built sometime in the 21st century. Plus Kirk might not have been making any effort to be precise with a semiconscious man.
But doesn't Khan specifically mention 1996 in TWOK?
Chekov said he was from the late 20th century, and never gave the exact year.
Khan's statement in TWOK of be from 200 years in the past (okay this is a stretch
) might be from no one ever correcting what Kirk first told him