The same thing happened to me. When I plugged in headphones, the sound was fine and when I unplugged them, it still kept showing headphones in the volume bar.
I tried mute \ screen rotation switch. Restarted ipad.
Then I launched Skype on ipad and made a video call without the headphones plugged in and it was back to volume (instead of headphones ringer), I opened youtube and the videos were playing with sound.