Visible crew/equipment: During the final fight, a steady cam operator with a white shirt and black straps around his body is seen during several wide angles. This is not a TV camera, it is a film crewmember. The Director even admits to it in the audio commentary on the DVD.
Visible crew/equipment: As Rocky is talking to Mickey in the locker room after his locker has been taken over by another boxer, you can see the shadow of the boom mic on the locker behind him as it dips in and out of view. As he starts walking away, you can also see it as it follows him.
Answer: They mean the entire year, 1976, is America's birth "day," being the bicentennial of the Declaration of Independence. So the fight, taking place on January 1, is the "first sporting event on our two hundredth birthday."