TMP_FILE='/ora/rman/scripts/tmp_chk.log'

chkbck ()
{
for i in `ls /ora/rman/logs/`;
do
        find /ora/rman/logs/$i/backup_a*.log -mtime -1 2>/dev/null
done
}

for i in `chkbck`;
do
        print $i
#        grep Exit $i

if egrep -i 'exit status [^0]' $i
then
        print "Backup Failed"
else
        print "Backup Successful"
fi
done > $TMP_FILE

OUTPUT
------

/ora/rman/logs/DBADB1D/backup_arch_DBADB1D_26Mar09-15:03:43.log
Backup Successful
/ora/rman/logs/DBADB1P/backup_arch_DBADB1P_26Mar09-12:15:15.log
Exit Status 1
Backup Failed

Kaapi:shell magvivek$ ls -lart
total 56
drwxr-xr-x  9 magvivek  staff  306 Mar 26 16:32 ..
-rw-r--r--  1 magvivek  staff   14 Mar 26 16:34 backup_arch_DBADB1D_26Mar09-15:03:43.log
-rw-r--r--  1 magvivek  staff   14 Mar 26 16:35 backup_arch_DBADB23D_26Mar09-15:03:43.log
-rw-r--r--  1 magvivek  staff   14 Mar 26 16:36 backup_arch_DBADB4D_26Mar09-15:03:43.log
-rw-r--r--  1 magvivek  staff   14 Mar 26 16:37 backup_arch_DBADBD_26Mar09-15:03:43.log
-rw-r--r--  1 magvivek  staff   14 Mar 26 16:37 backup_arch_DBADB2D_26Mar09-15:03:43.log
-rwxr-xr-x  1 magvivek  staff  583 Mar 26 17:51 somescript
-rw-r--r--  1 magvivek  staff  110 Mar 26 17:51 thislog
drwxr-xr-x  9 magvivek  staff  306 Mar 26 17:51 .

Kaapi:shell magvivek$ cat somescript
#reset the log file
rm thislog
#look for a particular pattern match. I guess from logfiles you provided
# the database Names start with DBA
ls -lart *DBA* | awk '{print $9}' | while read fname
do
#based on the sample you have give, seems 
#the dbname is third field, separated by underscore.
dbname=`echo $fname|cut -d"_" -f3`
#status is in last line
dbstatus=`tail -1 $fname`
#Just for Debugging
echo $dbname,$dbstatus 
#redirect the output to another file
echo $dbname,$dbstatus >>thislog
done
#mail it yourself, do whatever you want here.
#file will be deleted when called next time.

Kaapi:shell magvivek$ ./somescript
DBADB1D,Exit Status 1
DBADB23D,Exit Status 0
DBADB4D,Exit Status 0
DBADBD,Exit Status 1
DBADB2D,Exit Status 1

Kaapi:shell magvivek$ cat thislog
DBADB1D,Exit Status 1
DBADB23D,Exit Status 0
DBADB4D,Exit Status 0
DBADBD,Exit Status 1
DBADB2D,Exit Status 1

ls -lart *.log