I disagree. Sweat the details. It's what separates the good from the mediocre.
Consider an example. This is the technical drawing for the corner radius on an iPhone:
Note that it's not a simple circular arc. It has a subtle flattening of the curve where it meets the sides.
Why did Apple's designers do this? The difference is so slight you'd never notice them in hand. The easy thing to do would've been to just make it a regular circular arc.
I don't actually know why they did it, but I can speculate: I think by tapering the curve like that, that when photographed or rendered, it produces a gradient contour across the transition from the curve and the sides. It's a subtle effect, but it better conveys the sense of curvature and "hand feel," and makes for a sleeker, more premium looking product.
Of course, the vast majority of people will never consciously realize this. But they will say it "looks nicer," even if they can't articulate why.