Just a couple of weeks ago I noticed that all of the birthdays and anniversary's that I have in my contacts was showing up the day before on my calendar. Also any appts that I put on my calendar for all day and not at a specific time also shifted to one day earlier. It did not change any of the appts that I had at a specific time. Is their something wrong with the calendar because of leap year? How can I fix this issue? It says my system is up to date.

Have a look in Settings - General - Date and Time and make sure your Time Zone is set properly. The leap year idea is interesting, have a look also that your date and time is accurate. Let us know how you go.