How can I tell if my hourly cron job has run?

You should look in your /var/log/syslog log file. If a cron has run, it would have a line like:

Jun 11 19:09:01 penguin CRON[17376]: (root) CMD (  [ -x /usr/lib/php5/maxlifetime ] && [ -d /var/lib/php5 ] && find /var/lib/php5/ -depth -mindepth 1 -maxdepth 1 -type f -cmin +$(/usr/lib/php5/maxlifetime) ! -execdir fuser -s {} 2>/dev/null \; -delete)
Jun 11 19:17:01 penguin CRON[17799]: (root) CMD (   cd / && run-parts --report /etc/cron.hourly)

For troubleshooting tips, see https://help.ubuntu.com/community/CronHowto#Troubleshooting_and_Common_Problems

One major pitfall to cron is cron runs in an extremely limited shell environment, as a result a lot of variables aren't exported in to the environment, mainly $PATH. Make sure you use all absolute paths to executable, including common functions like echo, uptime, date, etc all need to use full paths (/bin/echo, /bin/date, /usr/bin/uptime). To determine the path to an executable, you can use the which command like so: which echo - this will show you the full path to that tool.

Try changing the first line of your script (the interpreter) to:

#!/bin/bash

I've also had problems in the past, with environment variables and PATH issues. After changing the interpreter to bash my issues were gone.