The classic rule...When it rains, no drains.This is a long-standing creed for a good reason. When you have a complex system draining large areas, it's amazing how quickly flow increases. Remember, walking in even ankle deep water can be extremely difficult if the current is swift enough, and water levels can rise very quickly in drains leaving you gasping for that last inch of air at the top as you wash towards certain death at a 30 foot waterfall around the next bend. Get the picture? In a similar vein, always explore heading against the flow of the water...if you get carried away you won't be launched into unknown deathtraps.
Shafts. Check step-irons closely. They'll often crumble in your hands or pull out of the wall. Test them before trusting your weight to them, especially in taller shafts. If the shaft is small enough diameter to comfortably chimney it, consider doing so if the irons look old or corroded, or feel unstable. "Chimney" is the word for bracing your back against the wall and using your feet against the opposite side and your hands against the back wall to move yourself up or down.
Funk. Be careful where you're stepping and what you're touching...if you get into areas of sanitary sewage ("sanitary" being the official word for stuff that isn't), it's common to end up with nasty bacterial illnesses soon thereafter. Also, any open wounds (including common things like dry skin which has cracked) can provide entry points for infection. In storm drains this isn't often a problem, but sanitary overflow may be present in normally "clean" drains at times.
Bad air. This is a concern in any enclosed space, especially drains. If people in the group start feeling sick, light-headed, dizzy, etc., get back out into fresh air ASAP. Don't count on smelling bad air; many deadly gaseous compounds have no odor. In addition to bad air, combustible gasses can be present. Think very carefully about open flame or sparks unless you're sure the drain is safe. And never drop a burning rag etc. down a shaft to test the air. This can cause not only structural damage but also personal injury if it happens to set off a fireball. Explosions which take out entire city blocks have been known to originate in drains so think twice. Additionally, keep in mind the ever-present possibility of industrial and bio-hazard waste being dumped in drains. If you start seeing hypodermics, bizarre sludge, etc. be careful.