In KeePassX 0.4.3, after checking as below (were clear) ...
Extras -> Settings -> Security
Show plain text passwords in:
[check] Edit Entry Dialog
[check] Database Entry Dialog
... passwords were shown in characters (as opposed to asterisks) in the "View/Edit Entry" windows and File -> Change Master Key window (the latter only when a password was entered).
Do the buttons with the sometimes greyed out eye icon work to toggle password display on and off?