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 'Items to Display' filter/tab in the top left of the calendar interface. Are 'Production Task Start Dates/Production Task Deadlines' checked off? If not, check those and click the green Filter button. Also, check your 'Team Member' filter drop down and make sure the check boxes next to your applicable team members are checked off. If not, check those and click Filter.
Remember that you can save your filter selections as a saved view using the Saved View feature.