If you can't seem to find a particular production task, or you're just not seeing production tasks at all on your calendar, there's probably a reason. First, check the 'Dates to Display' filter/tab in the top left of the calendar interface. Are 'My Production Tasks' and/or 'All Production Tasks' checked off? If not, check those and click Apply. Also, check your 'Team Member' filter drop down and make sure the checkboxes next to your applicable team members are checked off. If not, check those and click Apply.
Remember that you can save your filter selections as your default view using the "Set as Default" function under each filter/tab.