Arctic Sea Ice Decline
I've already discussed the issue of a secular trend inside of independent variation in the context of the ENSO (La Nina, El Nino) effects on atmospheric temperature. I pointed out there that many people don't seem to be able to follow the difference between the secular trend and the variation around it caused by events that have little or nothing to do with the trend itself. This confusion causes some people to swing around on global warming as the local independent variation goes up and down.
SkepticalScience.com has produced a great diagram that illustrates this problem. Here the secular trend describing the Arctic sea ice is negative, i.e., downward. People who aren't able to distinguish the random motion around the trend from the trend itself, and who are predisposed against global warming, seize upon the return of sea ice even though the secular trend is clearly downward. Every time it goes up they get excited. When it goes down their attention wanders elsewhere. They end up with an accumulated memory that the sea is increasing in spite of the reality that it's declining. It signals a fundamental defect in human reasoning that might defeat us. If enough people fail to understand what is happening, we may fail to act in time to oppose global warming.