Are there any references on the accuracy or (min/max/avg) error of Web Mercator when it comes to e.g. distance calculations?
For the sake of completeness, I haven't found any reference to the accuracy Web Mercator. In contrast, spatial computations in WGS-84 projection are, due to Charles Karney, highly accurate as described in http://arxiv.org/abs/1109.4448 This, however, requires Gnomonic projection of coordinates for point to line projections which is very costly in GIS software. An alternative is the use of de-facto standard Web Mercator which must be questioned if accuracy is sufficient.
Best Answer
As a first step, you could look at the distortions of the Mercator projection, which is a conformal projection. Distance with this projection is only correct along the equator, then the error increase with the latitude. Indeed, as you can see on a global view, the parallels keep the same legnth on the maps. For example, the horizontal scale factor, which is 1 at the equator, is equal to 1.15 at a latitude of 30° (15% error), 2 at a latitude of 60° and 11.5 at a latitude of 85° (scale factor 1/cos(latitude) )
Web Mercator uses WGS 84 Lat/Long as if they were angles on a sphere, presumably to reduce the processing time. This leads to more distortions, especially when you move away from the equator, that make the Web Mercator non-conformal. However,the impact of the "pseudo-sphericity" on distance measurements at high latitude is a lot smaller than the design of the Mercator projection.
The same reasoning holds for area distortion.