Asbestos. Unless there's positive reliable information as to absence of asbestos in the system, wear a respirator. Most institutional tunnels still have asbestos hanging around. Nobody can really say for sure at this point what asbestos will or won't do to you based on certain amounts of exposure (though its effect is definitely cumulative rather than immediate), but it is linked to an agonizing and untreatable lung cancer as well as other diseases. So, consider the risk and know that the effects of exposure are dramatically increased on those who smoke. Check the "equipment" section for specific info on respirators.
Machinery/miscellaneous equipment. Basically, don't touch any of this stuff. Turning valves, flipping switches, etc. can easily do more than just annoy someone who suddenly finds themselves without heating or some such. It can be hazardous for the explorer and for people topside; this is especially true for valves on steam lines. Never touch these. It may cause dangerous pressure changes in the line.
Personal security. This means, safety from the authorities. Keep an eye out for motion detectors, door-wired alarms, etc. It's a good idea to examine doors before opening for magnetic and wire detection devices. If you're an amateur please don't try to James Bond your way around security devices, you'll just draw attention to your fellow explorer's activities. Also, of course, be aware of security cameras. I don't know of any tunnels that have them, but many commons areas do, and the last thing the intrepid adventurer needs is to come out of a manhole on the Mall or a wall hatch in the Student Union and be smiling for Kampus Kops' Kandid Kamera.
Watch where you step...or lean, or crawl. When you're getting around and over and under and between the myriad pipelines which run through the tunnels, it's often tempting to use them as handholds, braces, even steps. You should avoid this in most cases. Always keep in mind...a steam line rupture anywhere in your vicinity of a standard ~250psi system is going to result in an inevitable lobster-style death for everyone around, and even relatively minor damage will likely result in tighter security (read: less fun), so think twice before sitting on that pipe.