I've noticed after upgrading to iOS 5 that a little pull-out sheet for the Calendar app appears on finger swipe near the top edge when inside other apps. I already disabled multi-gestures but this still occurs. Is there way to turn this off? It's annoying when using full screen drawing apps for example.
I think you might be talking about the Notification Center. Does it look like the pictures in this iOS: Understanding Notifications page?
If so, go to Settings -> Notifications -> Calendar, and turn off 'Notification Centre'.