java -jar FileChooserDemo.jar
Look&Feel: Nimbus
Dialog Type: Save
The "Save" button is displayed as "Save(S)" in Asian locale (where Save has been translated). In English locale, it's displayed as "Save" with no underline under S. In European locales, the underlines are also not displayed.

On the same demo, if we test "Open" button, the mnemonic has underline added to "Open(O)" and works fine.

The resource file looks like this:

% grep FileChooser.saveButton.textAndMnemonic jdk/src/share/classes/com/sun/swing/internal/plaf/basic/resources/*
basic_de.properties:FileChooser.saveButton.textAndMnemonic=&Speichern
basic_es.properties:FileChooser.saveButton.textAndMnemonic=&Guardar
basic_fr.properties:FileChooser.saveButton.textAndMnemonic=Enregi&strer
basic_it.properties:FileChooser.saveButton.textAndMnemonic=Sal&va
basic_ja.properties:FileChooser.saveButton.textAndMnemonic=\u4FDD\u5B58(&S)
basic_ko.properties:FileChooser.saveButton.textAndMnemonic=\uC800\uC7A5(&S)
basic.properties:FileChooser.saveButton.textAndMnemonic=&Save
basic_pt_BR.properties:FileChooser.saveButton.textAndMnemonic=&Salvar
basic_sv.properties:FileChooser.saveButton.textAndMnemonic=&Spara
basic_zh_CN.properties:FileChooser.saveButton.textAndMnemonic=\u4FDD\u5B58(&S)
basic_zh_TW.properties:FileChooser.saveButton.textAndMnemonic=\u5132\u5B58(&S)

% grep FileChooser.openButton.textAndMnemonic jdk/src/share/classes/com/sun/swing/internal/plaf/basic/resources/*
basic_de.properties:FileChooser.openButton.textAndMnemonic=\u00D6&ffnen
basic_es.properties:FileChooser.openButton.textAndMnemonic=&Abrir
basic_fr.properties:FileChooser.openButton.textAndMnemonic=&Ouvrir
basic_it.properties:FileChooser.openButton.textAndMnemonic=&Apri
basic_ja.properties:FileChooser.openButton.textAndMnemonic=\u958B\u304F(&O)
basic_ko.properties:FileChooser.openButton.textAndMnemonic=\uC5F4\uAE30(&O)
basic.properties:FileChooser.openButton.textAndMnemonic=&Open
basic_pt_BR.properties:FileChooser.openButton.textAndMnemonic=A&brir
basic_sv.properties:FileChooser.openButton.textAndMnemonic=&\u00D6ppna
basic_zh_CN.properties:FileChooser.openButton.textAndMnemonic=\u6253\u5F00(&O)
basic_zh_TW.properties:FileChooser.openButton.textAndMnemonic=\u958B\u555F(&O)