I will add my two cents, based on the two top answers in this 教えて!. Thanks to silvermaple for the encouragement.
It appears that one's 視点 is a direct point of view (visual or conceptual, as sawa noted) on a phenomenon. One's 観点, on the other hand, is comprised of underlying assumptions, ways of thinking, and experience considering multiple viewpoints.
For example, the first answer explains that changing one's 視点 might involve changing the angle or perspective from which one views or thinks about the phenomenon. Changing one's 観点, on the other hand, should involve a change in the underlying assumptions or way of thinking about an issue or object.
The second answer offers a simpler, yet easier to remember, explanation. It draws attention to the composition of 観 and 視. While 視 is a combination of 示 (show) and 見 (see), 観 comes from 鸛{こうのとり} (stork) and 見. 視 therefore suggests gazing a particular direction from a particular standpoint, while the stork in 観 opens her eyes and looks around, examining her environment from multiple angles.
Perhaps 観点 could be described as meta-視点.
見方{みかた}
and立場{たちば}
.見方
is "way of looking at things", metaphorically emphasizing how you come to your point of view.立場
is "standpoint", metaphorically emphasizing your place in relation to the thing you have a point of view on. Hope that helps. :)着眼点【ちゃくがんてん】
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