cron logs its action to the syslog facility ’cron’, and logging may be controlled using the standard syslogd(8) facility.
That seems to tell that cron uses the system logger to create it's logs. The relevant file, I guess, is /var/log/syslog
which you need to go trough to see what (possible error) messages cron has produced. Read the man page I referred to for more information, and possibly any syslog man pages:
for more information.
The other option is to make the cron command create somekind of output to tell if it succeeded; for example the below line would run date
and if it succeeds, create (an empty) file called success
to /home/somebody/ (and if I'm right, failed date
causes the file not to be created..and if the file already exists, it's time stamp is updated):
3 * * * * /bin/date && touch /home/somebody/success