The iPad Mini is supposed to have edge detection software that prevents the kind of problem you are describing. If the usual fixes (listed below) don't solve the problem, I'd take it into an Apple Store (if you have one nearby) and demonstrate the issue. If they can't fix it, there is a good chance they will swap out your iPad for another (hopefully) problem free unit.
Be sure to make a appointment. Apple Stores can be busy.
You can also work through their online support, but the Store is by far the more satisfying experience.
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The usual fixes:
When you have problems with an app it's a good idea to clear it from RAM.
Close/Clear the app: With the problem app closed, double tap on the Home button to get the multitask bar. Tap and hold on any icon in the bar until they jiggle, then tap the minus sign on the problem app. This will remove it from RAM and insure a clean start the next time you launch the app.
If that does not work try a restart,
Restart: Hold down the power button until the power off slider appears. Slide it off. When the iPad finishes shutting down, hold down the power button again until the Apple logo appears. Apple recommends you restart the iPad at least once a month.
and then a reset if that does not work.
Reset: Hold down the power and home buttons until the Apple logo appears. The iPad will reboot. This usually takes a bit longer than a restart.
Reset All Settings: Another, somewhat more drastic thing you can do is Reset All Settings. You'll find this under Settings > General > Reset > Reset All Settings. It won't erase any of your content, apps, or accounts; but you will have to go through most of your other settings and re-tweak them back to your liking.