I am surprised that no one mentioned that it's the length of the extension cord, not the distance from the 'service outlet' that makes the voltage drop, thus slowing the door down, thus making for longer retraction times.
This is not true. The voltage drop across an extension cord's length is no different than any other conductor of equal size. The reason why voltage drop is typically more of an issue with extension cords is because they are undersized for their respective length. Also, the majority of the voltage drop can also occur at the slip-fittings of the plug and receptacle. (The cheaper the cord and/or outlet, the higher the voltage drop across the plug.)
The issue of voltage drop as it applies to the actual appliance is overblown in many cases. This is because the service voltage entering a structure can vary so greatly for different parts of the system and throughout the country.
As for the "Reaction Time" of the door opener, my first impression is that the inspector didn't understand what he was saying (and hiding it with technical-sounding gibberish). The door will "React" the same regardless of the over/under voltage condition...specifically for the reason that such conditions will always exist. The door position controller does not use timed-feedback, so the speed of the door (i.e. motor) does not alter positions.
As for the opening/closing speed, because the opener has a significant gear reduction, broad changes in motor speed will translate to proportionally small changes in door speed.
Or Garage Door Opener
