Is one accelerometer enough for detecting tilt/orientation of a rigid body?
The accelerometer allows the device to know which way is up and which way is down. So when the display is vertical, it is totally trivial to orient the display correctly. If the display is on a level table, and then rotated slowly, the accelerometer is basically useless. Some devices also have either a three axis magnetometer or at least one angular rate sensor (gyro) or both. These can help with detecting rotational motion that the accelerometer is not good at detecting. So if the display is vertical, there is no problem. If it is then tilted to a horizontal plane, the accelerometer is out of the picture.

But if the device has a chip gyro or magnetometer, it can detect a quick rotation and cause the display to rotate also. Most of the time this is correct (the quick rotation was caused by the user turning the display while horizontal), but sometimes it is an annoyance (maybe you turned a corner quickly, and the display then suddenly went sideways).

In theory having two accelerometers with some baseline between them would allow you to detect angular rotation, but I don't think that is done in practice, and I don't think it would actually work, because it would require a level of precision that consumer accelerometers don't have. The chip gyro gives you much more bang for your buck. For total dead reckoning, you basically need a 3-axis accelerometer and a 3-axis gyro or angular rate sensor. Very precise electronic dead reckoning devices exist, but they are expensive, and subject to export control in the USA (because they can be used in missile guidance systems).