When you click save on a file, it will to something every time, even if it's not exactly visible.
Since this was brought up, a ticket for marking files as "save pending". Icon to indicate the status would be great, possibly also a pending counter.
To answer the original question, just change the id3v2.3 as the tag format from picard options and choose the encoding you need. Then just load the music to picard and re-save. As luks said, eventhough it appears that picard doesn't do anything, it actually re-saves the files.
Whenever I re-save a lot of files, I usually alter the path to which the files are saved, so that I can monitor the moving process from windows explorer. As soon as all the files have been moved to their new location, they have also been saved and I can close picard. Then I'll just rename the folder so that my mediaplayer can find it again. It's a roundabout method to use, but it works and I don't have to guess when the saving is finished.