Examples : world projection (Mercator, useless), lack of metadata (dates of the images ?), choice of labels at medium scale (especially with the 'Relief' maps).
Such discrepancy between good graphical precision, esthetics and geographical imprecision, lack of quality information are misleading a large part of the public.
I know I've used it, to find, research and understand the layout of, Actual Locations on Earth, more than once. I never even stopped to think about the projection.
It would be interesting to hear what you feel would be different in the end-user experience if the projection was changed.
De-zoom and look at the apparent continent sizes, it's just horrible. Half of emerged lands in antarctica ? Groenland the size of Africa ? Think about children exposed to those maps before a good atlas is showed to them.
I co-wrote a paper about this topic, but it's in french :
A technical choice (summary : it's easier to have perpendicular parallels and meridians) has prevailed upon a geographical choice. It's not very complicated to link the projection to the scale of the view, all serious geographical internet portals are doing so (IGN, Ordnance Survey, etc.)