I recently updated the app (12 Sep) and I haven't been able to change the filenames since. This is the error I'm seeing
I've tried opening the folder using ⌘O and also opening the app with root (sudo open "/Applications/Mp3Tag.app", and also changing the permissions of the files themselves.
Have a look at this thread and see your problem is similar:
Also, a search for "secure bookmarks" in the forum may lead to more threads.
Can you try this command via Terminal.app while Mp3tag being closed:
defaults delete app.mp3tag.Mp3tag SecurityScopedBookmarks
After that, load the folder (not the individual files) via ⌘O and see if the issue persists.