Ny way to make Console prompt for authentication to logs the user isn’t authorised to

It's found in the secure.log (the path is /var/log/secure.log) and the entries would look something like this:

authorizationhost[5917]: Failed to authenticate user <cksum> (error: 9).

It does not log password attempts (the password they tried to use), just the actual unsuccessful (or successful) login attempt.

Additionally, to focus your search exclusively for failed login attemps, open Terminal.app (found in Utilities folder) and run the following command:

sudo grep 'Failed to authenticate' /var/log/secure.log

It's trying to start the nonexistent apps.

From the console entry com.apple.launchd.peruser.502 we know it's trying to start on behalf of user (instead of system or administrator) that has UID 502.

You can get particular user's account name with id -u -n 502.

I'd look at following places:

Login items

Go to System Preferences->Users & Groups. Choose appropriate user and select Login Items tab.

Look if you recognize uninstalled applications in the list and delete them. You have to select the app and press '-' beneath the list.

Launchd

Start the terminal. Enter launchctl list and see if you find uninstalled apps in there. False entries can be removed by launchctl remove label, for example launchctl remove de.novamedia.NML2NDeviceObserver.

Repeat the process, but this time prepend sudo to commands, like sudo launchctl list, to catch all the apps executed in system context.

You can find out more about launchd and launchctl by entering man launchd and man launchctl.

Launchd configurations

Look into following directories (from man launchctl):

1. ~/Library/LaunchAgents - Per-user agents provided by the user
2. ~/Library/LaunchAgents - Per-user agents provided by the administrator
3. /Library/LaunchDaemons - System wide daemons provided by the administrator.
4. /System/Library/LaunchAgents - OS X Per-user agents
5. /System/Library/LaunchDaemons - OS X System wide daemons

If you find a file referring to uninstalled app, remove it (you'll need to sudo rm for items in 3, 4 & 5).

More about those files in http://developer.apple.com/library/mac/#documentation/MacOSX/Conceptual/BPSystemStartup/Chapters/CreatingLaunchdJobs.html especially 'The launchd Startup Process'.