How to find archivelog gaps in the backups
I think that REPORT is the appropriate command, but at the moment I cannot test it. Before you execute the report command you should execute a CROSSCHECK command so that rman does actually know which backups exists and which are missing.

If you want to find out if there are archive log backups missing then 

REPORT NEED BACKUP DATABASE;


should do the job. The whole database must be backed up because of the missing archive logs the database cannot be restored to the current point in time. So the command will report all data files.

If backup pieces were destroyed that contain datafiles of the morning full backup then 

REPORT NEED BACKUP DAYS 1 DATABASE;


So this command will report both problems.

The report-command is documented in the Backup and Recovery Reference and in the Backup and Recovery User's Guide.

So all in all do

CROSSCHEK BACKUP;
REPORT NEED BACKUP DAYS 1 DATABASE;