The primary reason for examining any residual plot is to see whether the rough is rough enough or whether it contains additional smooth.

Data = Fit + Residual
Data = Smooth + Rough

As John Tukey explained:
"Here the fit is our current description --always incomplete, always
approximate--of the overall behavior of the data. Each individual
observation is split up into a sum of this fit and what is left over,
called a residual.

Residuals are our main tool in going further. They are to the data analyst
what powerful magnifying glasses, sensitive chemical tests for bloodstains,
and delicate listening devices are to a story-book detective. They permeate
all sorts of data analysis and appear in many guises.

[...] For us the most useful plot will be one that might reveal the
unexpected or the unobvious. Sometimes a plot "in the large" will do this.
Usually, however, it is the plot of residuals that has the greatest use and
the greatest impact."