You might remember a few weeks ago when we covered a story from Gizmodo that suggested that Apple's new iPhone 5S had major issues with its positioning sensors being pretty far off. Today Gizmodo released a report that explains why the sensor data is so far off from proper calibration.
It appears that Apple has switched manufacturers of its motion sensors from the 5 to the 5S and a difference in how the sensors measure bias is causing existing apps to be off by several degrees. The previous iPhone models use sensors from STMicroelectronics and the new iPhone 5S features sensors from Bosch. Simply put, the sensors are calibrated different, resulting in a need for different coding.
Since Apple did not account for this change during the hardware calibration phase, devs must now account for it in the coding of their apps. Apps would need to be individually calibrated by the user which requires each app to be updated with new code. While this is a pain in the rear, it appears to be the only known fix at the moment.