I decided to reinstall the program, that did not fix the issue. But it did retain my changes to the settings. So I went looking for the user settings file, and deleted it, and that has fixed the issue. Since that meant that the problem was caused by one of the changes I made, I started making the same changes again, this time documenting whether the problem had returned after each step. The setting that caused this was Tools -> Preferences -> Appearance -> Look and Feel -> Nimbus. I guess that option...
Each time I open a file, whether Freemind is already open or not, all nodes and all paths on the map load twice, almost on top of each other, like a dropshadow. This seems to be a purely visual change, and returns to normal as soon as I select any node, or scroll or pan in any direction. However, at the same time that this began, the "control" + "up arrow" hotkey, which moves the selected node up relative to its siblings, stopped responding, which is much more of a problem. The opposite hotkey, "control"...