Yes, you should absolutely be able to ride in the rain and wash the bike (though the manual does state to not use pressure washers). The charger, motor controller, motor, and BMS are all designed to handle moisture and water spray .. but the BMS may have a design flaw.
It's worth noting too that while the bike shows symptoms of being affected by moisture (disabled throttle when damp, resets had no effect, worked fine the next morning), I don't know for sure that's the problem. The board certainly looked fine when I pulled off the front plate, no obvious corrosion or dirt buildup on the actual board.
When Zero contacted me, they assured me that it was definitely covered under warranty. I could either bring it to a Honda or Yamaha dealer and Zero would have them handle the disassembly and board replacement or I could do the swap myself. I opted for the latter, so Zero is sending me a new revision of the BMS, a loaner laptop with tools to flash the new board, and taking the old BMS back for analysis. I'll report back when/if I hear what the cause was.
I've ridden a handful of times in the rain without problems before, and Harlan stated this is the second BMS fault that he's heard of .. the first being one he encountered, but a reset was able to get him going again. So this isn't a common problem. I don't mean make people unnecessarily worried.. just aware.
_If_ it is a design flaw in the BMS and not something peculiar to my bike, I would suppose Zero would have to replace all the boards in the shipping bikes. They've certainly demonstrated good customer support to this point, let's see how this plays out.