Have you got notifications muted ? Only notifications (including games) get muted, so the iPod/Music and Videos apps, and headphones, still get sound.
Depending on what you've got Settings > General > Use Side Switch To set to (mute or rotation lock), then you can mute notifications by the switch on the right hand side of the iPad, or via the taskbar : double-click the home button; slide from the left; and it's the icon far left; press home again to exit the taskbar. The function that isn't on the side switch is set via the taskbar instead : http://support.apple.com/kb/HT4085
Try going into General again, but with your headphones off.
The reason is that you can have two options or configurations of sound volume, one with headphones, other without. So if you have your headphones on and turn the volume to full blast, when you simply try to take headphones off, volume changes back to what it was set to WITHOUT headphones.
Couldn't find mentioning of these configurations on the user guide, had it discovered accidentally.