Just like we think about a Plan B when running rivers, we should give some thought to a Plan B for the overall trip. River levels, weather, people, etc. change - sometimes despite our best plans. Let someone that is not on the trip know about your planned itenerary and make certain you call them afterwards to let them know everything turned out fine. It doesn't hurt to think about evacuation routes like nearby trails and roads. Where is the nearest hospital? Perhaps carry a cell phone in a Pelican Box in case your car is stolen or towed.
The Lead paddler (Scout/Probe) must keep tabs on paddlers behind them. If the group gets too spread out, it is time to take a break to close the gap again. If someone gets pinned, blow the whistle and perhaps head to shore to help out.
The Sweep boat is the enforcer. They need to push people along to keep the trip on schedule. If an accident occurs, they have great visability and can often get to the victim rather rapidly. In some cases, you may take charge of the rescue and delegate rescue responsibilities - Sam & Alice: Get Sally to shore, Tim: you work on the boat, Pete: Please deal with the paddle, Rich: Set safety below, etc.
When planning the trip (and participating for that matter), think about whom you are paddling with. Take a bit of time to learn about their paddling experience and skill level. What kind of equipment are they carrying? During the river trip, keep an eye on the party. If you feel someones needs a bit of assistance, offer it in a polite way.
Look for the telltale markers that the river is rising or falling and plan your actions accordingly. If the river becomes too high - suggest walking out. Others may be thinking the same but don't want to lose face - they will be very thankful. Research rivers you plan to paddle via guidebooks and web resources like American Whitewater. Pay close attention to known hazards like sieves, permaainers, undercuts, etc. so you can safely avoid them. Always bear in mind, rivers change sometimes dramatically at different levels and after flooding has occurred. Use your best judgment.
What if the weather changes rapidly - believe me it happens, especially in the mountains. Thunderstorms on large bodies of water require you to get off the water and move away from the shoreline. If it turns cold, dis you pack some extra food, water, and insulation? If a serious injury takes place, you may need to build shelter and assign a pair of paddlers to seek help.
It is always a good idea to let someone you trust know about your plans and follow-up with them once you are finished. Let everyone know the rough schedule for the trip so they can help you stay on schedule. This becomes even more important on Winter runs when the days get surprisingly short. Monitor your progress so you can shorten breaks and river play to pick up the pace. Let everyone know when you plan to meet at the put-in and don't wait too long for stragglers. I like to use email to communicate trip plans - it can be very effective.