EDIT: There is now a partial solution for this here.
The good news is that this low-level Android bug largely affects developers or people who work in Bluetooth dev shops who have been around a large number of Bluetooth devices in the same place. Going to a BLE or iBeacon hackathon will almost certainly a trigger it. Fortunately, most end users of our apps do not do this.
The bug is triggered when an internal buffer holding recently scanned Bluetooth LE Mac addresses fills up. After it fills, scanning a new Bluetooth LE device will cause Android's Bluetooth service to crash and restart itself. The dialog you see is from Android's Bluetooth Share service, which dies not cleanly handle the restart of the Bluetooth Service restart and crashes itself. Here is the Android bug report.
The bug can affect any app or library that does Bluetooth LE scanning, or looks for iBeacons, not just the Android iBeacon Library. But again, not all users will experience it. I work at Radius Networks where we have dozens of Bluetooth LE devices transmitting all the time, and it took four months before I ever saw that dialog on my Nexus 4 -- it only came up two weeks ago. Since then, I have been working to characterize the problem and find workarounds.
I have been able to clear the condition simply by going into Airplane Mode for a few seconds then coming out. This, however is not a permenant fix, as overflowing Android's buffer again will cause it to return. We are still researching more automated solutions.