HI
Shut iPad down by holding BOTH the 'Home' button and 'power' button at the same time, until its lights go off. Then restart just using the power button. This should iron out this annoying glitch.
Initially I had no sound on headphones using skype, though the iPad sound worked when headphones were removed.
Tried headphones on 2 different devices and they worked on both sides, proving headphones were working fine.
Persisting with skype 'test call' and my headphones (RHAs plugs with microphone and volume control), I got white noise that would only disappear from the iPad on mute. Again the white noise stopped when the head phones were removed and the iPad's sound was normal. I removed the skype app, but the problem was accross any program using sound, including iTunes.
I moved the 'balance' setting: access via 'General', 'Accessibility', scroll down to 'Hearing' you will see the slide, button should be central. Reading the reply where this worked I tapped the 'L' and setting moved there, then I tapped the 'R' and the setting moved there, then I tapped the dot between the 'L' 'R', this placed the setting central.
I then shut down iPad as described: Holding 'home' button & 'power' button until the iPad shut down, after the restart the problem had gone. Clear sound through the head phones. I do not think it was app related.
Hope this helps...Good luck.