That's weird. If you already set all day events to "None", you shouldn't get alerts. Of course you can disable the events in the Calendar app. Or you could try the usual fixes. They might remove this glitch.
Reset your iPad. This won't change settings, and data won't get lost. To do so press and hold Home and Power button simultaneously until the Apple logo appears. Release both and let the iPad power up.
Force close the Calendar app:
Double tap the Home button to reveal the multitask bar. Slide the picture above the Calendar app icon to the top of the screen.
Restart your device:
Turn it off, wait for a few minites and turn it on again.