Running as an admin user. I used to be able to use Disk Utility to verify permissions, but now there is only a single First Aid, which told me the disk is OK.
Anyway, the problem seems to be that there is only one parameter in the app's memory for both Open Image and Open Test Image. Here's what com.findmyfont.Find my Font.plist looks like:
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "www.apple.com/DTDs/PropertyList-1.0.dtd">
<plist version="1.0">
<dict>
<key>NSNavLastRootDirectory</key>
<string>/Library/Fonts</string>
<key>NSNavPanelExpandedSizeForOpenMode</key>
<string>{704, 459}</string>
</dict>
</plist>
The NSNavLastRootDirectory key apparently serves for both. There should be two different keys.
Added in edit: But after deleting the plist file, Find My Font still remembers the same directory, still only one directory, and doesn't create a new plist file. What gives?