Setup Local Mail and get cron job output mails
When a cron job starts successfully or fails to execute for some reason cron daemon automatically sends an email to the user who set the cron job. That mail contains the description of a successful job or the detailed report why the particular cron job failed.
If your local mail system is not set you will not receive those mails. The cron job output emails will just die in a local mail spool folder. So you need to set up your mailer daemon to read those mails. See this answer on How read local email in thunderbird to get all your local mails.
If your cronjob fails you will receive a mail stating the reason of failure. This is one of the best way to detect the error in setting a cron job.
According to this answer one can get errors of a cronjob in a log file using redirection. But you need to set the redirection with your cron job and specify the log file by yourself.
/var/log/syslog file is always there to check if your cron job is running as you expected or not.