I like the idea of an open carry picnic. Just a few suggestions. One is I'd suggest very careful selection of the site. Hold the picnic on private property if possible. Another point on location I'd suggest is holding the event outside of city limits, that removes the need for participants to have permits to legally carry openly. Doing those two things reduce the possibility of some government entity using the event as a means to snoop around, hassle participants, etc. I suggest this because of my "healthy" distrust of the government. It also allows the organizers to use private property rights, and the more remote location, to discourage protesters and have better control of any media coverage. If anyone causes trouble the sheriff can be called to remove the trouble maker for us since that would be a matter of trespassing.
Another suggestion might be obvious but I'll say it anyway, the picnic should have a strict "no alcohol" policy. This gets back to avoiding legal issues, we don't need accusations of minors in possession, intoxicated while armed, or public intoxication. It would also avoid some public perception problems. We don't need to see a picture floating around the internet of a person with a gun on their hip and opening a beer. It could be a very innocent act of an open carry participant opening a brew for a non-carrying friend but we should not have to be put in the position of trying to defend that image.