"By the way, chance of rain refers to the percent of the area that's expected to receive rain, as I understand it."
Chance of rain = (probability that it will rain somewhere) x (percent of area expected to receive rain, if it occurs at all)
If there is a 40 percent chance of rain, then "the correct way to interpret the forecast is: there is a 40 percent chance that rain will occur at any given point in the area."
"I wonder what the stats are for weather pattern change and instability in light of global warming? Could it be that the computer models used for forecasting need some adaptation, or perhaps it is more chaotic?"
I think one of the primary reasons weather forecasts may be inaccurate is due to a lack of data. If they could have weather instruments every 100 yards that supply real-time updates and if they had massive computing power, I think their predictions would be more accurate. Also, if any one is like me, they don't remember all the times the forecasters were right - just the times they were wrong.