A hesitation when accelerating from a full stop can be caused by a couple things.
If the scooter is fairly new or hasn't had much use, the brake may be sticking. The brake pad is a metal alloy with a rubberized ring around the outer edge. When the unit is new the rubberized material will sometimes stick to the brake pressure plate. When the brake is manually released it will sometimes be necessary to rock the scooter back before the pad will release. When throttle is applied the power to the motor must first brake the pad loose before it can move the scooter. It is usually a very minor hesitation and is much more noticeable when the unit is being powered without a rider. This should become less noticeable as the unit is used. If the problem persists there may be a problem with the brake and it will need to be replaced. (BRAKE REPLACEMENT)
The throttle potentiometer will sometimes cause a hesitation. The potentiometer will sometimes develop a dead spot on the low end and will not apply power to the motor until it is advanced past the dead spot. Most often this will cause the unit to not run and send a throttle pot fault code. You can check this by doing the output to motor test. Press the thumb bar slowly forward and monitor the output to the motor. It should rise evenly as you press the thumb bar.
Hesitation is often reported from customers who have had an older analog Pace Saver and have recently acquired a new digital Pace Saver. The digital controllers are programmed for a softer acceleration and deceleration to help soften the pitching of the rider back and forth while driving.