I'm a retired Master watchmaker with Rolex experience.
First, as an older watch, it's almost certain that the Tritium dial and hands will need replacing since they will likely no longer glow.
The luminous dot on the bezel may or may not be replaceable. At one time Rolex would only replace the entire bezel.
By now, the watch will need all new case and crown water proofing gaskets to insure there are no leaks.
The movement will need a complete clean and oil.
The band may need to have the clasp replaced, depending on how bad it is, but can likely be repaired.
Your best bet on all this is to send the watch to the New York service center.
BE SURE to clearly specify that you want the watch serviced, the band repaired, the bezel dot replaced, and the dial and hands.
As part of the servicing, Rolex will replace all the gaskets, the crown, if necessary, and clean, oil, and adjust the movement, polish the case, test it's water resistance, and in general refurbish it to near-new condition.
If you want to spend a few more dollars for a worth-while upgrade, request a mineral glass crystal.
Older Rolex's often came with a plastic crystal, and the mineral doesn't scratch up nearly as bad.
All this will cost some money, but you'll have one of the finest watches ever made, back in like new condition.
I DO NOT recommend using a Non-Rolex repair service. Some are great, some are phonies. You usually have no way of knowing which for sure.
With Rolex, you do, and they'll do it RIGHT.