I stated my concerns about iOS7 here.  I found the following three bugs in my first four hours of use. One is a game stopper, the other two are easy to work around.
First:

I am guessing this picture shows a broken call of some kind. It is likely that the way this application did logins either changed or was deprecated in iOS7. I present this to show a broken app. Is it necessarily the FAULT of iOS? When I upgrade and lose functionality I do not focus on fault, but rather, why is this broken?

Second:

I was using two fingers swiping up to close multiple apps at a time. Several times I had this happen. The preview flew off the screen, but the app was still running. It happened with multiple apps, and sometimes did not happen to an app it had happened to previously.

Third:

Notice in the bottom right hand corner the directory has two striped background colors instead of the gradients used elsewhere. All three of these bugs happened on an iPad mini and an iPhone5.