Living in Florida I deal with very (very) sporadic weather. I've been to shows that have rained nearly the entire time and ones that have been torrential for about 5 minutes and then the sun comes out. Then others were like last week where there was not one cloud in the sky.
For rain:
Make sure your MP soap is completely covered. It will sweat very badly in the humidity of a rainy day. It has to be wrapped with a tight seal. Your CP soap will also sweat so be prepared for that. They won't wart like a MP soap will though so that's a nice plus.
Make sure you have tent weights. I use plastic sand bags. Don't put up any vinyl banners onto your tent if it is especially windy. It will act like a sail. You can instead attach it to your table.
I second the tarp. I always keep 2 blue plastic table cloths with me when there is any chance of rain at a show. In the event of rain, I quickly cover my table. I should consider the clear ones though! I've never thought of that!
And yes, take plastic tubs. I have big Rubbermaid tubs I can throw everything into quickly if I need to.