1) Beware of the door zone when riding past parallel parked cars. Often times, new riders are mainly concerned with the moving vehicles, causing them to ride as far to the side of the road as possible. But an unexpected door being opened can a cause a nasty crash, or throw the cyclist into the path of the moving vehicles. See the Wikipedia entry for some illustrative pictures.
2) Beware of sudden and unexpected right turns. In countries where people drive on the right side of the rode, the right turn is easiest and quickest of turns. Drivers often make a right turn without signaling and without checking their shoulder. Unfortunately, this often takes them directly across the path of the bike lane.
3) Look at the wheels of cars to figure out what they are going to to do. I always think of cars as big dumb slow animals that can really mess you up once they get their speed up. So it very important to figure out what their "intentions" are ahead of time. You can detect a rolling wheel much more quickly than you can determine if a car is in motion by looking at its body. You can also see if a car is preparing to turn by the angle of the wheels.