I got this fixed professionally, but I probably could have done it myself, given the following info:
It turns out the beep is caused by a corroded sensor. The sensor is a small circuit board on the lower tray, it senses when there is a leak. In actual fact, the dishwasher was not leaking at all, but water was dripping onto the lower tray. Dripping occurs when you stop the dishwasher mid-cycle to put in that coffee cup you forgot in your bedroom. When you stop the dishwasher, it holds the door locked for two seconds so that most of the water on the internal lid drips off, but it is impossible for it all to drip off so, when you pull out the drawer, you get drips on the tray underneath (and the sensor). The water, mixed with dishwasher detergent, is very caustic and after a while the caustic chemicals corrode the sensor and cause it to malfunction. The dishwasher may stop (it shuts down if it detects a leak) or, if the sensor is stuffed, it will beep and the blue LED will turn red and flash and beep.
In the first pic you can see the lid (obviously this stays put when the drawer is opened, allowing drips) The 2nd picture shows the new sensor installed by Fisher & Paykell (looks like the new ones are covered to prevent drips). You can see the corrosion from all the times I opened it mid-cycle (even though I was told not to :) what harm could opening the door mid cycle do, eh? I assumed it was a safety precaution.. )
Do not open drawer-style dishwashers mid-cycle, under any circumstances. Also do not put tall objects in that would prevent the lid from descending all the way when the draw is closed - the lack of seal will allow caustic water to leak out as it is being sprayed around.
You may be able to repair this problem by cleaning up the mess, inspecting the sensor for corrosion or deposits of detergent, etc and getting rid of it. Repair any broken or corroded contacts.
If the damage is bad, you will probably need a new sensor board from Fisher and Paykel.