If you want to monitor successfully sent mails, enable debugging to email module:

1. Log in to the DSM console.
2. Look for the following logging parameter files:

   For Windows: <dsm_installation_folder>\jre\lib\logging.properties
   For Linux: /opt/dsm/jre/lib/logging.properties

3. Append the following debug option at the tail of the file:

   com.thirdbrigade.commoncore.email.level=ALL

4. Restart the DSM service.

The log will now be written to <dsm_installation_folder>\server0.log.

Below is a successful mail log sample:

Apr 07, 2015 12:44:46 PM com.thirdbrigade.commoncore.email.SMTPMailer connect
FINE: ThID:87|TID:0|TNAME:Primary|UID:-1|UNAME:|Connection made successfully.
Apr 07, 2015 12:44:46 PM com.thirdbrigade.commoncore.email.SMTPMailer send
FINEST: ThID:87|TID:0|TNAME:Primary|UID:-1|UNAME:|Sending mail as UTF-8: false
Apr 07, 2015 12:44:46 PM com.thirdbrigade.commoncore.email.SMTPMailer send
FINE: ThID:87|TID:0|TNAME:Primary|UID:-1|UNAME:|Server Response: 250 2.6.0
 
<1113530168.0.1428381886323.JavaMail.root@VM-Simon-DS95-DSM>
  
[InternalId=12841952215041, Hostname=NJ-Core-DC.cncorelab.com] Queued mail for delivery
Apr 07, 2015 12:44:46 PM com.thirdbrigade.commoncore.email.SMTPMailer send
FINE: ThID:87|TID:0|TNAME:Primary|UID:-1|UNAME:|Mail was sent successfully.

Below is a failed mail log sample wherein the SMTP server is down. You may observe other error messages if the root cause of the issue is different:

Apr 07, 2015 11:16:31 AM com.thirdbrigade.commoncore.email.SMTPMailer connect
SEVERE: ThID:40|TID:0|TNAME:Primary|UID:-1|UNAME:|Exception caught connecting to SMTP server :
 Could not connect to SMTP host: 192.168.26.85, port: 25
Apr 07, 2015 11:16:31 AM com.thirdbrigade.manager.core.scheduler.jobschedulers.jobs.EmailJob onRun
SEVERE: ThID:40|TID:0|TNAME:Primary|UID:-1|UNAME:|SMTP Mailer Exception caught:
 
com.thirdbrigade.commoncore.email.SMTPMailerException: javax.mail.MessagingException:
Could not connect to SMTP host: 192.168.26.85, port: 25;
nested exception is:
java.net.NoRouteToHostException: No route to host
at com.thirdbrigade.commoncore.email.SMTPMailer.connect(SMTPMailer.java:439)
at com.thirdbrigade.manager.core.util.EmailUtilities.getConfiguredSMTPMailer(EmailUtilities.java:136)
at com.thirdbrigade.manager.core.scheduler.jobschedulers.jobs.EmailJob.onRun(EmailJob.java:54)
at com.thirdbrigade.manager.core.scheduler.jobschedulers.jobs.Job.run(Job.java:149)
at java.util.concurrent.Executors$RunnableAdapter.call(Executors.java:511)
at java.util.concurrent.FutureTask.run(FutureTask.java:266)
at java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1142)
at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:617)
at java.lang.Thread.run(Thread.java:745)
Caused by: javax.mail.MessagingException: Could not connect to SMTP host: 192.168.26.85, port: 25;
nested exception is:
java.net.NoRouteToHostException: No route to host
at com.sun.mail.smtp.SMTPTransport.openServer(SMTPTransport.java:1972)
at com.sun.mail.smtp.SMTPTransport.protocolConnect(SMTPTransport.java:642)
at javax.mail.Service.connect(Service.java:295)
at com.thirdbrigade.commoncore.email.SMTPMailer.connect(SMTPMailer.java:424)
... 8 more
Caused by: java.net.NoRouteToHostException: No route to host
at java.net.PlainSocketImpl.socketConnect(Native Method)
at java.net.AbstractPlainSocketImpl.doConnect(AbstractPlainSocketImpl.java:345)
at java.net.AbstractPlainSocketImpl.connectToAddress(AbstractPlainSocketImpl.java:206)
at java.net.AbstractPlainSocketImpl.connect(AbstractPlainSocketImpl.java:188)
at java.net.SocksSocketImpl.connect(SocksSocketImpl.java:392)
at java.net.Socket.connect(Socket.java:589)
at java.net.Socket.connect(Socket.java:538)
at com.sun.mail.util.SocketFetcher.createSocket(SocketFetcher.java:319)
at com.sun.mail.util.SocketFetcher.getSocket(SocketFetcher.java:233)
at com.sun.mail.smtp.SMTPTransport.openServer(SMTPTransport.java:1938)
... 11 more

You may use the "com.thirdbrigade.commoncore.email.SMTPMailer" keyword to filter the logs, and then "successfully" or "Exception" to check the successful mail sent.