Okay, did some comparing and it appears only ALL DAY events are displaying on the wrong day. Anything I have set with a specific time shows up on the correct day. Found a reference on the Internet that explains this.
Apparently, according to that source, the computer considers a day to START at 12:00 am, so an all day event displays on the computer on the correct day which begins at midnight. But the iPhone considers a day to END at 12:00 am so all day events are posted BEFORE midnight of the correct day, which is the wrong day.
What I don't understand is WHY Apple has the iPhone using different criteria than their computers? This "bug" apparently goes back to the original iPhone iOS. Why haven't they reprogrammed it by now?
I have an appointment with Apple for next week to have someone call me and I will discuss it with them. Hopefully, they'll have an answer for me on how to fix my events to display correctly. If not, I guess I'll have to change all day events to begin and end at specific times. Which means deleting birthdays from the Address Book and creating calendar entries for each one. What a nuisance that will be!
ETA: AND I won't be able to rely on the US Holidays calendar. *sigh*