Adding video and audio via the 'Add Media' button is glitchy. If you insert a video or audio shortcode it doesn't display, unless you also upload and insert a similar file.
If you insert a video already in the Media Library and then upload and insert an audio file, the audio would display but not the video. To get the video shortcode to display you have to upload a video file (you don't have to insert it, just upload it) on the same post/page.
If you had a page of videos and audios then you would have to upload an audio and video file for them all to be displayed. They don't have to be the same format though, as when I uploaded a .MOV file all the .M4Vs loaded.
Additionally, when I inserted a .MOV file (recorded for testing purposes via QuickTime) it just inserted an empty video shortcode tag (i.e. [video][/video]', rather than than degrading to a flash player or something if unsupported. I don't know if there is a flash fallback in place but I assumed so as on the Twenty Thirteen demo site the audio file is displaying via a flash player.