The Mute button works differently in iOS 6, it won't allow you to watch videos with sound in certain apps

  Outside changes to the auto-brightness system, Apple changed and how the Mute button works from iOS 6, some realizing that the songs or movies they are trying to listen to have no sound. Basically, Apple would have modified some things through its iOS, and when the Mute button is activated, some applications do not play the sound of video clips or songs. Safari is excluded because it is a native application, browsers fall into the same category, but applications that have an integrated web browser, called web views, will not run sound if their developers have not configured them correctly and do not update them in the near future.

  This web views system is used by Twitter, the iDevice.ro application and many others, but so far I have managed to reproduce the problem only in the Twitter application, which I assume uses a different system for playing sounds. The iDevice.ro application is not affected, you can hear the sounds of the video clips even when you have the Mute button active, but I assume that the Facebook application and others similar will not allow the same thing. Only certain applications are not compatible with the change made by Apple, it remains for you to discover them as you use them.