In iOS 6.0 shouldAutorotateToInterfaceOrientation is deprecated and never gets called. Can be reproduced the simulator.
More info and possible fixes: http://stackoverflow.com/questions/12260261/shouldautorotatetointerfaceorientation-not-being-called-in-ios-6
This means that UIViewComponentPeer::displayRotated() never gets called in JUCE and the display is not rotated correctly.
For now I have just added a hotfix to JuceUIViewController. Hopefully this will get fixed in the repository soon
JuceUIView* juceView = (JuceUIView*) [self view];
jassert (juceView != nil && juceView->owner != nullptr);
[UIView setAnimationsEnabled: YES];