Normally I can redirect the intended output with a command into a file similar to:

crontabcommand >/ust/local/www/mylogfile

But what happens if the crontab job aborts without having the chance to
write some output into the logifle (e.g. because /usr/local/www/ does not exist
or the syntax of the command is not correct).

I guess these kind of basic information are written to some extra system logfiles.

Where can I find the system logfile for the crontab jobs. When which crontab job was
started and if it is exited with witch error.