If you are going east or coming from the east, there is a new customs/immigration office at Gun Creek in Virgin Gorda Sound. Very easy and convenient; hooray for progress.
If you are leaving the BVI with no intention of returning on this trip, you will not need an air ticket out. It's no problem to fly in on a one way ticket if you are an American, as the USVI are so close; perhaps you'll need a ferry ticket, though.
There are very few places you can enter in the Caribbean, without your clearance papers from your last port, the French islands being the exception.
As mentioned above, the vessel or captain is responsible for repatriation of any crew who may be departing the vessel in any country other than their own, so always list crew as passengers on inbound clearance to avoid this problem. To cover my own as* though, I always require a cash bond equal to anyone's air ticket to their country of origin, if I don't know them and they are sailing with me.