Someone else should really add some new tips. Mine can only be so useful.
1. If you drove to the race alone, use a safety pin to secure your car keys in a jersey pocket.
2. A trunk-mounted bike carrier makes a decent workstand.
3. The key to climbing a muddy hill is weight distribution. Typically, you'll want to shift your weight forward when climbing to keep the front wheel on the ground. However, if your rear tire is slipping, you need to shift back a little more to give it some extra traction.
4. You probably don't gain anything by running, or even walking, a hill that you can climb on the bike. We had a nasty hill at the end of the lap, and a lot of people were getting off their bikes. I climbed it the first lap and was really wiped by the time I got to the top, so the next two laps I ran/walked it. The result was, I was still winded at the top, and half a dozen people had passed me. The last lap, I rode it and nearly passed out, but I gained several positions.
My tips are getting pretty lame. Somebody else should update this thread and add something useful.