I have had nothing but problems since changing from iOS 6 to 7 on my iPad (3rd Generation), especially the 7.0.2 version released about a week or so ago:
1) Audio problems when hardwired to Big Jambox, which wasn't an issue with iOS6, yet no audio issue when using Bluetooth (or when hardwired to my regular Jambox); go figure;
2) Video streams are sometimes out of sync with audio to varying degrees no matter the provider (Amazon, Netflix, NBC app) when using Bluetooth and external speakers (but not when hardwired to the same speakers);
3) While using many apps, they close by themselves while I am doing tasks within the app;
4) For no apparent reason, iPad rebooted on its own the other night, which I never recall happening with iOS 6;
5) When I unplug external speaker wire from iPad, the last song played in iTunes starts playing all by itself! (i seem to think this also happened with iOS6 too).
Going to try the System Reset (as outlined by Philly_Phan) on this forum and hope that does the trick. Jawbone (the company that manufactures Jambox) told me the other night that they are getting "lots of complaints" re the Big Jambox and compatibility with iOS 7, which is interesting.
No issues with the Big Jambox (or regular model) hardwired or using with Bluetooth on Android Galaxy S4!