Baldur's Gate : The Sword Coast Chronicles : NWN2 Persistent World

A quick question - what is the best way to trash items while dungeoneering?

Also, with the 'new' chest system, what happens if I leave a crap item in the chest, is that a problem? What if I drop more crap items from my inventory into the chest, is that a good way to dump items?

no problem, just leave or put trash into any chest/crate/bones.

I think anything that is left is transferred to the next person who opens the chest, but I could be wrong on that.

The best way in my opinion is to set up a campfire using the PC tools menu, throw stuff into it, and then use the same system to dismiss the campfire.

Leave stuff in the loot chests in the dungeon. When the chest locking timer fires, anything left inside will get deleted automatically (about 5 mins)