Here are some 'layers/additions' that I think could be considered:
1) main rivers
2) more lakes
3) some more islands
4) different shades for mountains/hills
5) different shades for deserts
6) different shades for glaciers
7) include parts of antarctica
8) triangles for highest mountains of continents
9) 'lines' for panama and suez canal
10) have 2-3 versions that correspond to different projections
If I had to pick three, I'd go for 1, 4 and 10.
Some of these suggestions would work on more detailed maps for sure, and I think a few more islands and lakes could be added to the main map. However, I think the simplicity of the map should be kept, since it's not that necessary for most quizzes which use it.
I would only be favorable to add more islands and lakes (just like I did on some of my maps) on the standard JP world map but nothing more.
In my opinion, it has to be kept simple and close to its original purpose: making people guess countries.
Another idea would be to propose another standard map, more consistent, including your suggestions for quiz about physical geography and so. I would support this!
Click 100 Geographic Features on a World Map.