Check the power supply to the motor - one of the wires is always live when the ignition is on. This provides power to take the wipers to the park position after you have switched them off. If the power supply is OK, you have nothing to loose by taking the motor apart and cleaning the switch. If there is no permanent supply you will need to trace it back.
I have this same problem and its not much of a pain when its really raining but when its misty, it's worrysome. I now have adequate wiring diagrams so I will test and rebuild, as required, over the holidays.
Please report back as you debug your D, and I will do the same.
Personally, I enjoy the challenges. Rebuilding a non-repareable switch is a fun challenge. :-]
Right now, I am rebuilding a 1918 White Monoplane engine. For that project there are no replacement parts. They all have to be made. And since this is a hobby and hobbies are a voyage, not a destination, the repairs and making the parts are part of the hobby. So if the wipers don't park and it is the switch, I will attempt to repair or remanufacture the parts first. My D-I is for fun AND my daily driver. Fortunately this is not my only car and I can drive the Bimmer while putzing with the D-I wipers.
BTW, anyone need the schematic for the wipers? I can post it to a web site, if desired.