I seem to have trouble posting anything to the ESRI Community Pages unless it is a Question.
But this isn't a Question; it is a solution to an issue I'm sure has happened to others.
In some of our recent map products, certain Polygons would express wayward, scribble-like lines that did not exist in our Maps but would appear on Layouts. And the Exported Map Files for viewing/printing.
The exact appearance of the stray lines is dependent on the Scale at which the Map is viewed, but all other factors seemed negligible.
Trial & Error revealed the common denominator being features with more complex symbologies: Negative Offset Effect Values.
Offset Effects themselves are not necessarily problematic. Certainly, changing the Offset Effect Option from the default "Fast" to "Accurate" can relieve a lot of unexpected cartographic effects, even if it does take a bit longer to render.
But if you are using a Polygon symbolized with a Negative Offset Effect Value, removing that particular stroke (or the negative value) will resolve the wayward scribbles in your Output Files.
The Responsible Symbol Option; Stroke Disabled
Polygon without wayward scribbleys
Disable polygon symbology strokes utilizing a negative offset value. Or alter that value to anything zero or above. See initial post for examples and details.