Where do you report serious flaws with iOS7?
You can provide feedback to Apple regarding iOS at Apple's feedback page relevant for the device that you wish to feedback for:


http://www.apple.com/feedback/iphone.html
http://www.apple.com/feedback/ipad.html
http://www.apple.com/feedback/ipodtouch.html


If you are an Apple Developer, you can report bugs using Apple Bug Reporter.