I also have an iPad mini with iOS 8. I have not experienced any of the problems listed above, but my Wi-Fi connection is slow, I cannot create events in Calendar without problems, my Multitasking Gestures sometimes don't work, the Multitasking screen appears with a delay, and Keyboard shortcuts disappear after I restart my iPad.
The problem that I am experiencing with Calendar: When I try to create an all-day event, it will make the event start 1 day earlier than I specified and end on the correct date. So every time I create an all-day event, I have to go back to the event to correct the start date and move the end date back by 1 day. For example, if I created an all-day event for today only (20 September), it will instead create an event for 19-20 September.
The Multitasking Gestures problem mainly occurs when I want to access the Multitasking screen from the Home Screen. I swipe up with four fingers, but most of the time it doesn't work. When I double-click the Home button, I have to wait around 1 second before the Multitasking screen appears.
After I installed iOS 8, I noticed that my keyboard shortcuts were not working. I checked them in Settings and they were gone. I added them back, but after I restarted my iPad a few days later, I once again noticed that they were not working. As soon as I opened Settings, they appeared and have been working since.
I am hoping that Apple will fix these bugs, as they are rather annoying!