I download a movie on my iPad mini. Where do I view the movie?

You may not have the right format for the video. If that is the case the file will be copied onto the iPad but will not appear in the movies app as a file that can be played. See the following support document for information on what formats are supported for the iPad. iTunes: Frequently asked questions about viewing and syncing videos - Apple Support

Also, if your file isn't supported by Apple, try looking at third party viewers that are available in the App Store. VLC player is a good one. http://www.videolan.org/vlc/download-ios.html