Reports, confirmed by both Gizmodo (forgive the linkbait title), Ars Technica, and myself, are surfacing that state that the iPhone 5S’ accelerometer, compass, and gyroscope — all of which are part of the M7 chip — appear to be improperly calibrated.
This particular issue is easily replicable: simply go in to the Compass app, calibrate your device, and swipe to the left to reveal the leveling function. Set your device on a flat surface, like a desk. My personal device shows that a flat surface of zero is off by three degrees. Others are off by varying amounts, though none appear to be anymore than off by eight degrees.
Don’t hit the panic button yet: the problem is almost certainly fixable by a software update. Does your iPhone 5S suffer this issue?