I have had this problem in previous versions of the iOS 9 beta on my iPad Air, and I just experienced it with the GM on my iPhone 6. My iTunes password isn't working. I tried to download an app from the App Store, copied and pasted my password from 1Password, and it was rejected. I tried this from the Settings app as well. I also manually entered it in, and it was rejected. I know the password is correct because I just used it to sign into the forums. I had this issue on my Mac on a previous beta of El Cap.
I signed out of the account in Settings, and signed back in. That worked. Then, I tried to download an app from the App Store again. It was rejected.
Has anyone experienced this? I can't do anything regarding iTunes on my phone, which is obviously a huge problem.