Judging from multi-error coins in which the rotating die can be ascertained, it is the hammer die that is almost always responsible. That is contrary to longstanding expectations, but expectations are often wrong.
Rotated die errors can be dynamic or they can be fixed. Or you can have a series of dynamic rotations followed by a series of fixed rotations, and vice versa.
Rotated die errors can arise from:
1. A die that becomes loose.
2. A die that is installed wrong.
3. A die that becomes loose and is tightened back up in the wrong position.
4. A die on which the "flat" is ground in the wrong place, which promotes installation in the wrong postion.
It's clear that the shallow flat does not significantly impede rotation.
Error coin writer and researcher.