Trigger control.
Sight picture and sight alignment are important, but trigger control more so. The pistol floats in the holding pattern, and trigger pressure is increased slowly, smoothly, steadily, straight to the rear, subconsciously, until the shot breaks. The shot will land within the holding pattern. The smaller the holding pattern, the tighter the group.
Sight picture/sight alignment errors result in the group being larger. Trigger control errors produce those stray shots that are out of the group, low and left for a right hander.
The shot must break without disturbance to the pistol.
"Live and dry" is the single best training exercise. A partner loads/or does not load the pistol. The shooter does not know if the pistol is loaded. The partner does not load a round into the pistol until the shooter is consistently dry firing without the pistol being disturbed. The point is that there is no difference between a dry shot and a live one. In a live and dry practice, only 10-20 percent of the shots should be live, and then only when the shooter is firing strings of dry shots.
An optic sight eliminates sight alignment, leaving sight picture and trigger control. If dry firing with an optical sight, any disturbance to the pistol when the shot breaks is readily apparent.
A laser is also a great training aid. The shooter and the coach can clearly see the dip resulting from poor trigger control.