This thread is really old, but I'll reply anyway.
Nitric acid is an oxidizing agent, and actually has more oxidizing power when dilute than when concentrated. If there are any reducing agents present in solution when you dump it in, it may explode. If the material is basic, it could heat up and splatter material everywhere. If it has a lot of carbonate in it or some other material that produces gas upon reaction with acid, it could splatter/explode. The least likely (and perhaps most easily thought of) reaction to produce an explosion would be an actual nitration.
My question is, did the student pour the nitric acid into the organic waste container or the inorganic container? That would make a big difference.