I'm assuming you figured this out already but:
Technical Reference for Log Files in Configuration Manager
That's a list of client-side logs and what they do. They are located in Windows\CCM\Logs
AppEnforce.log
will show you the actual command-line executed and the resulting exit code for each Deployment Type (only for the new style ConfigMgr Applications)
This is my go-to for troubleshooting apps. Haven't really found any other logs that are exceedingly useful.