The video from the late 1980s of graduates at the Harvard commencement explaining why it's hotter in summer than winter (because the Earth is closer to the sun!) is available online for free here -- click on the VoD symbol in the lower right corner. To be precise, it appears that 21 of 23 randomly interviewed Harvard graduates, professors, or alumni got wrong at least one of two astronomical questions (Why are there seasons? and Why are there phases of the moon? Because the Earth's shadow falls on the moon!)
One thing you'll note from the video is that the Harvard grads sound much, much more confident in their wrong answers than the working class kids at the local high school. I guess that's the Harvard Edge!
One thing I've noticed is that most people don't have much sense of when sunset comes at different times of the year, even though that directly affects their lives. I have a pretty good knowledge, probably because golf courses charge lower rates in the later afternoon, so it's important to golfers to know how much daylight there is to tell whether you can finish on time. For example, if the cheaper twilight rates begin at 1pm in January, that's actually a worse deal than twilight rates beginning at 2pm in May, because you are unlikely to finish 18 holes in January, but will have plenty of time in May. Yet, few golfers have much specific sense of how long the days are.
Another problem people have is getting terrible sunburns in spring because they don't realize how strong the sun is. I recall going with a bunch of Rice science and engineering majors to the beach at Galveston on April 9th and we all got fried because nobody put on any suntan lotion. That made me realize that even though April 9th seemed like a long time before summer, the sun is actually as high in the sky then as on the Labor Day weekend (i.e., 19 days after the vernal equinox is the equivalent of 19 days before the autumnal equinox, or about September 2). May 1, being about 40 days after the spring equinox is the equivalent of mid-August in terms of sun strength, so even if the weather is cool, watch out for how strong the sun is.
During the first energy crisis in late 1973, Time Magazine ran an editorial saying it was completely obvious that we should have year-round daylight savings. Congress complied, and a few months later Time ran another item denouncing Congress as complete chowderheads for not realizing how late the sun came up in winter. Didn't they look at an almanac? There was no mention of Time's endorsement of year-round daylight saving less than half a year before.
Year-round daylight savings time was quickly junked. Now, Congress is now considering adding a month more to daylight savings time in the fall and another month in the spring. I suspect adding a month in fall is a poor idea because DST already goes five weeks past the autumn equinox, so mornings will be awfully dark by Thanksgiving, but adding to it in the spring makes sense because it currently doesn't start until 2 weeks after the spring equinox.
The reason for the current asymmetry in daylight savings time is that it's generally colder on, say, the spring equinox (about March 21) than on the autumn equinox (about September 21) because temperature lags behind amount of sunlight. Still, I suspect, the current seasonal asymmetry in daylight savings time is too large and adding a few weeks in the earlier spring would be a net benefit.