How do I Increase the log level of Fetchmail?

From fetchmail(1) (man 1 fetchmail):

Increasing verbosity of output:

   -v | --verbose
          Verbose mode.  All control messages passed between fetchmail and  the
          mailserver  are echoed to stdout.  Overrides --silent.  Doubling this
          option (-v -v) causes extra diagnostic information to be printed.

About debugging to syslog:

   The  --syslog option (keyword: set syslog) allows you to redirect status and
   error messages emitted to the syslog(3) system daemon  if  available.   Mes-
   sages are logged with an id of fetchmail, the facility LOG_MAIL, and priori-
   ties LOG_ERR, LOG_ALERT or LOG_INFO.  This option is  intended  for  logging
   status  and  error  messages which indicate the status of the daemon and the
   results while fetching mail from the server(s).  Error messages for  command
   line  options and parsing the .fetchmailrc file are still written to stderr,
   or to the specified log file.  The --nosyslog option turns off use  of  sys-
   log(3),  assuming  it’s turned on in the ~/.fetchmailrc file, or that the -L
   or --logfile <file> option was used.

Hope that helps!

at least in Debian you can also run

/etc/init.d/fetchmail debug-run

fetchmail will log directly to console and not fork into background