Communication is the key really.
My main concern is to keep away from potential hazard of falling climbers. Stay well behind so if a climber falls he wouldn't land on you. Rappel is generally easy because it is controlled way of going down and then getting close to a climber let him know about your intentions. Ask to hold and wait if it gets dangerously close. In most cases it is possible to rappel on the side of the climbing route. But if not communication is the key.
Sometimes it happens that one party is moving much faster than another. If you notice that ask to get way or offer to go first. It really has to be said, don't expect that another party will notice that they are blocking the way. For them it is irrelevant so initiative naturally should come from party behind. Of course you can wait or be a dick and overtake on a pitch.
Post edited at 13:03