Use event.modifier. What sort of key do you expect?
I would expect something that helps to determine which modifier was held down when clicking (e.g. Shift, Control, Alt), but event.modifier returns a boolean which is mostly false (as I found out that it evaluates to true when Shift-Control is held down while clicking). This will help me at first, but anyway I would appreciate knowledge about how to find out which specific key was held (maybe not even a modifier but a character key like "f"). Possible?
To detect shift, use event.shift. See the documentation for more information: http://livedocs.adobe.com/acrobat_sdk/9.1/Acrobat9_1_HTMLHelp/JS_API_AcroJS.88.604.html
There's no way to know what other keys are pressed when a button is clicked.
It's also very helpful to know that there are no other ways if this is a fact.