First, I'd like the cold opening to be a scene from an early on TOS episode. Maybe a digest version of the last 2 acts of Balance of Terror, though it would be kind of tough to speed up the tension from that episode and not to mention a little sacrilegious.
Then during the opening credits they can do some quick cuts of episodes from the original run. A quick shot of Kirk and a Gorn, Spock with a goatee, the Enterprise firing on The Doomsday Machine, etc...
After the credits you can do a quick mention of Janice Lester and then start a whole new story set during TOS' 4th season.
Oh, another thing I'd like to see is a little wear and tear on the Enterprise. She's been out there a few years so let it show. I'd liked Voyager but to me not dirtying her was a big drop of the ball.