I am using the projection EPSG:3857 to plot out points on the map. Since the Earth is closer to the shape of an ellipsoid instead of a sphere, I am interested to find out what is the range of error if I were to plot some points using this spherical mercator projection. Using examples of prominent points of interest such as the tip of Mount Everest, Statue of Liberty, etc, would be helpful.
As long as you project from the source SRS to EPSG:3857, then the point position will be accurate (to within the projection accuracy - some are a bit "off"). Projection from EPSG:4326 to EPSG:3857 should be very accurate - a few metres at the most. Size of objects will obviously be in error depending on latitude.