My friend was booked on the CPT-AMS flight on KLM which departs at 00:30 or so, so he booked the flight for lets say Feb 5 (I don't know the exact date) and went to the airport after packing on the fifth to catch his flight. He found out that he missed his flight since now it was the sixth at 00:30, the next day. So he missed his flight by 24 hours, I believe KLM rebooked him on the next flight out.
The dumbest thing I have done is I booked a flight from YYZ-AUH departing at 21:45. Without realizing it, I thought the flight departed at 11:45PM. I got asked by my friend who was driving me to the airport at around 6:30 what time my flight was leaving at and he's like your flight is a 9:45PM, not 11:45. Suffice to say, I had to rush to finish getting ready and had a mad scramble to the airport (30min drive) and no dinner.
Moral of both stories, always double and triple check your flight times and dates.