I've had to let my Zero sit out in the rain sometimes in Seattle's rainy season, and the only problem I've noticed is with the bolts on the (OPTIONAL) rear luggage rack. I've sprayed them a bit with anti-corrosion coatings to keep them as fresh as possible. The bike itself has very little exposed places to tarnish.
I think the one issue is that riding in the rain can get the belt dirty, which leads to a soft growling noise if you use a lot of torque until it gets clean and dry again.
Like any motorcycle, if you intend to leave a bike out in the rain for a length of time, use a cover. I've used
kwiKover before but it relies on an easily removed sportbike seat. Perhaps I'll figure out how to install it now that I have more experience with the bike.