We had similar issues (just got it back from the stealers actually - hopefully they'll have actuallly fixed it this time), wipers would come on very slowly (by themselves), sidelights would come on, central locking wouldn't work. All these faults happened with engine off.
I traced it to water in the fusebox, and sodden relays.
This was traced to a leak from the windscreen, through the aerial, and also somewhere on the bulkhead.
Do check your dash-top storage bin (the one directly between you and the windscreen) to see if it's damp or wet. Water drips down from there, directly onto the fuse box apparently, causing shorting and corrosion on the terminals on the relays and main bus.