Editing your cron jobs with the crontab -e command will ensure that your crontab is at least syntactically correct, by not installing it unless it is a valid cron file.
Outside of that though, it falls to you to test that your jobs are in fact running correctly. This can be achieved by piping the cron command output to a file that you control for each one of your jobs.
In practice:
00 01 * * * bash mycommand1.sh > /tmp/mycronjob.log 00 02 * * * bash mycommand2.sh > /tmp/mycronjob.log
And in the same vein, you can check that the crontab as a whole is being executed by creating a job right at the end of the cron list that runs every minute and pipes out its output to a file that you control:
*/1 * * * * echo "Success! $(date)" >> /tmp/cronwatch.log
Note that > means rewrite the target file every time, whilst >> means append to the end of the file (and create if not exist).
Nifty
Related Link: https://help.ubuntu.com/community/CronHowto