Although Chekhov was not yet part of the crew in the 1967 Star Trek episode ("Space Seed") where the Enterprise first encounters Khan, Khan recognizes Chekhov in this film when they first meet on Ceti Alpha V.
When the Enterprise is flying into the Nebula in the chase scene, all of the crew reacts as if in a collision, yet Capt. Kirk remains still. Guess he was too good to fall around like the others.
Check out the blood stain on Kirk's tunic in sick bay. If you watch it closely, it bounces around from production mistakes so much that it will actually ruin the scenes once you notice it.