Safari 8 fails to play any (mp4) video in-browser
It could be caused by a corrupt or incompatible video codec or interfering third-party software. Playing MP4 video files should work in any browser.

Here is what you can try…


Installing the latest OS X Yosemite Updates also updates the Quicktime framework which is used by Safari. Safari loads video Codecs from the /Library/Internet Plug-Ins directory. So make sure Safari is updated by going to App Store -> Updates -> Safari (version 10.x is the latest version).
Make sure that the Internet plugin-ins checkbox is enabled. Safari -> Preferences -> Security -> Internet plugin-ins -> Allow Plug-ins

Does using a browser with Flash built-in (like Chrome) allow you to play mp4 files? If so, try deleting or updating Flash in System Preferences, which could fix Safari. 


If none of this helps, just try switching to a different browser (popular ones include Chrome, Firefox, Vivaldi, and Opera) or a different WiFi network.