I found this bug on Ubuntu (12.04) with OpenJDK 1.6. This bug is not evident on Windows or Mac with Oracle Java. I didn't test right now on Ubuntu with Oracle Java.
Sometimes Drop-down menu of Open File (or similar Open Project or Add Raster ayer) seems to works fine: a) click on the arrow, b) drop-down menu remains on the screen and users can choose the type of file.
But after using some times "Open Files" or similar (included Open Wizard), randomly, drop-down menu stops to work. This is the behaviour: a) click on the arrow, b) drop-down menu cames out, c) if user realise mouse menu, drop down disappears and user cannot do any choice.
Drop-down menu remains evident on the screen only if user leaves the cursor on the arrow with left button (of mouse) presse: the only way, in this case, to choose type of file is to use keyboard up-down keys with a hand (using the other to press on the drop-down arrow of the menu.
By the time that this behaviour comes out it remains until user closes OJ and reopens it.