The most distal (brown) is usually the most wide bore and should be used for blood draws (esp. if you are calibrating a SvO2 monitor), CVP measurements, and blood administration. I don't have a particular order to use any of the others, so I kind of just go from there. Oh, and I almost always relocate drips and what not because half the time, anesthesia doesn't check compatibilities (their idea is that if it doesn't turn white immediately, it is fine)... well, needless to say, that makes me nervous, so I run compatabilities and go from there.
Sometimes a doc will specify to leave a port open for TPN use only. That only happens on occasion.
The only problems I can think of that you would run into if you are disconnecting are 1) increased risk for infection if strict aseptic technique is not used, and 2) if the patient is on pressors, the disconnect, no matter how fast, can cause a drop in their pressure. Oh, and make sure if it is a pressor in line on one of the lumens, that you withdraw the med/blood in a 10 ml syringe prior to flushing it to avoid bolusing them with it.
Sometimes a patient will come up and have a "manifold" with a random mixture of all sorts of intraop meds running in it. I will typically leave the mainfold up at least until the patient is stable and then begin disassembling the different lines into proper (compatability checked) lumens. It really ticks off the anesthesia personnel when you take down their manifold and then the patient emergently has to go back to OR