Removing imperfections in circle with color gradient edge

One approach would be to draw a red disk and then filter it to blur the edges:

GaussianFilter[Image[Graphics[{White, Disk[], Red, Disk[{0, 0}, 0.5]}]], 20]

This is, more or less, what Photoshop would call "feathering" of the red region into the white background.

Alternative approaches:

1. RadialGradientImage:

RadialGradientImage[{Red, White, White}, ImageSize -> Medium]

2. ParametricPlot + ColorFunction + Blend

ParametricPlot[r {Cos[t], Sin[t]}, {r, 0, 1}, {t, 0, 2 Pi}, 
 Mesh -> None, BoundaryStyle -> None, Axes -> False, Frame -> False, 
 ColorFunction -> (Blend[{Red, White}, #3] &)]

3. ChartElementDataFunction "GradientBubble"

Graphics[ChartElementDataFunction["GradientBubble", 
   "ColorScheme" -> (Lighter[Red, #] & /@ Subdivide[4]), 
   "GradientDirection" -> "Radial"][{{0, 1}, {0, 1}}]]

4. Blur

Blur[Graphics[{Red, Disk[]}, PlotRangePadding -> Scaled[.2]], 50]