I have experience dealing with fiducials where hovering over them with the cursor will “nudge” them slightly to a new position. It was clearly visible in the slice window when this happened. Not sure if this is exactly what you mean by sometimes “might move on its own”. It was weird behavior that I never really understood and appeared more common after saving fiducials and then loading in again. I know this behavior existed in Slicer 4.8.1 though might still be present in the current code.
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