Somehow it seems to be a total breakdown. Nothing seems to work anymore properly. The only thing that seems to work properly is the recording of visits/actions/etc. in the DB.
The problem is that your config.ini.php or your global.ini.php contain the following:
logger_message = screen
which logs all messages to the screen.
Instead, global.ini.php should contain
;logger_message = screen
and you should remove this from your config.ini.php if it is there.