Here's some things that have come to my head, some are peds-specific, others are more things for internship in general:
*Along the lines of going around on your patients in the middle of the night and looking at fluid status before you go to bed (as was posted earlier), I like to go around to the nurses' stations of all of the units I'm covering and ask if they have any questions before I try to lay down to get some sleep. I can't begin to tell you how frustrating it is to try to lay down and then get paged for something 2 minutes after you lay down. Doing this before going to bed takes maybe 10 minutes at the most, but it can save you some small calls late in the night.
*Listen to nurses and parents, no matter if something they say sounds like the silliest thing in the world. As an intern, nurses usually have the experience advantage on you, especially in the subspecialty fields (think Heme-Onc, Cardiology, NICU, etc.) and will know when a kid needs your attention. Also, lots of parents seemingly have a sixth sense for when their kid is just "not right", and even if you don't think it's particularly bad, show the parents that you are taking their concerns seriously.
*It's a great release, but overall, don't bitch and moan about how your schedule sucks or how you got screwed over on something schedule-wise, it happens to everyone and all you do by complaining is waste energy.
*Communication is the key to everything. This means between you and parents as well as anyone involved with patient care (attending, fellows, other residents, students, etc.). The more you communicate, the less likely something unforseen is likely to arise. Just like another poster said, use your upper levels for guidance, and if you're ever unsure about something, let them know because it's much easier for them to give you advice then instead of later on when all hell is breaking loose. Also, don't be afraid to say "I don't know", you'll be much safer if you accept this and look for advice from the people above you.
*Whenever you are getting a consult, have a plan in mind in terms of what made you get the consult and what information you would like to get out of the consulting service. Example: don't just page the cardiology fellow and say "I need a consult because I hear a murmur", explain to them how you have interpreted the murmur (location, grade, pitch, etc.) and how getting a consult will add to the management plan (i.e. an echo will not only tell you the etiology, but help guide your decision on follow-up).
*Remember that most of your patients are going to be young children, and when they come into the hospital, they are often nervous and so are the parents or other family members. It goes along with the communication point I made above, but talking your way through a physical exam and explaining why you're going to do labs or other tests on a child goes a long way towards building trust between yourself and your patient as well as the family.
*Finally, you're going to work a lot of hours in your intern year, but make sure you take some time for yourself to enjoy things in your life outside of medicine. For me, these things include going out to dinner with my girlfriend at least once a week, keeping up with 24 and the Amazing Race on my Tivo, and playing golf as much as possible. While you may feel that your entire life is focused on residency, having this actually occur is not healthy at all, so learn to keep other activities in your life and you'll be a happier person, and probably a better resident at the same time. Hope this helps some people out.