How can I use RMAN to show if there are archive logs that need to backed up? My main concern is knowing if the Oracle Archive Logs haven't been backed up in a while because something is broken that I may not know about.

When I query v$log it appears to be good with First_Time being very recent.  I would think v$log wouuld have lots of rows if the logs had not been backing up.

SELECT * FROM v$log; 


Shows only a few, two say current (four returned).

select * from v$log_history order by FIRST_TIME desc;


Shows lots.
You can do this from RMAN.

list archivelog all backed up 0 times to disk;


or

list archivelog all backed up 0 times to sbt_tape;


Depending on the backup method you use.