Improved rendering quality of the minimap by gogoalex · Pull Request #1431 · mapeditor/tiled
Looks like it's possibly using nearest neighbor when drawing the minimap - as the minimap shrinks, each tile is represented by not an average of the pixels in the tile, but a couple discrete pixels picked from the tile. If the tile has high contrast, you can easily end up with the selected pixels not looking very much like the tile as a whole. A solution could be to use a resampling mode like bilinear interpolation in the drawing of the minimap.
(disclaimer: I have not looked at the pull request, nor do I know very well how tiled's code works, I'm just going off of the images and my own experience with the minimap. If I'm off base feel free to disregard).