I have the same issue. Below my discription of the problem...
Rogue alerts are added to Calendar events (iOS 5.1.1) which I make in iCal (OS 10.8.2) and are synced via iCloud.
The alerts are set for both timed events and all day events. Alerts are set for either 0:00am on that day or at the start of the event!
When I look in iCal for the specific event there is no alert set, however when the alert syncs via iCloud to my iPhone4S there is an alert set for this event!! Highly undesirable to say the least. To avoid the alerts from going off I have to manually cancel it in the iOS calendar event.
I checked that the standard alert settings in both iCal and iPhone are off. Tried to toggle on and off on both sides, with reboot inbetween. Then checked with a default setting of 5 mins in advance but then the iPhone synced event gets 2 alerts; 1- with 5 min notice and the rogue one at the start or at 0:00 😟
The strangest thing is that this only happens to my iPhone4S, where my wife is also subscribed to this agenda using her 3GS. Hence new event made on iCal syncs via iCloud to my 4S and her 3GS only sets a rogue alert on my 4S!!
The problems started to occur when I opened my Calendar app a week ago, upon which the app did not show any events. I had to reboot my iphone in order to get the app working again. It seemingly had lost all the events since it gradually started to import them from iCloud again... All seemed fine until the alerts started in the middle of the night 😟
Please help