I have the same problem on my iPhone4. It is obviously a bug in the software. Once it pops out I am locked out of my phone. I can't even begin to describe the frustration this causes. All that stuff about holding down the buttons is useless. the phone won't even shut off. I can take a screen shot like that or go to voice control. Even when I got to a wifi connection, I can't get on. This app blocks everything else. This is a serious bug and can have serious consequences. The only thing my phone would do is go to voice control and let me play iTunes or phone people. Some smart phone hey?
I have finally got to a place with a wide enough wifi to connect my computer and restore the phone. This has lasted over a day!
I don't even know why Find My Friends is on my phone. Is it part of the package and how do I turn it off?