I'm trying to rotate an object's face and keep having the problem where it will not stop shaking, even if the mouse is moving.
My first idea is than you have "Snap tool" ON. Check Magnet icon (in horshoe shape) on 3D Viwe bottom bar. Next to "Proportional editing". Keyshort is "Shif+Tab". Can be easily switched accidentally.
If this don't help you, consider uploading your .blend. Because we can only guess now.