What's compression?
As you near the spead of sound, you're pushing an enormous shockwave through the air in front of you.
When you pass the speed of sound, that shock wave is behind you.
In between, in the so-called "trans-sonic" region, the shock wave appears around the aeroplane at different points, as the speed of the air differs at different points (fast at the wing roots, slower over the canopy, for example). This shock wave greatly interferes with the airflow around the control surfaces, sometimes locking them in place, sometimes making them useless, sometimes reversing their effect. The net result is a joystick set in concrete - an unresponsive plane - and it's why in some planes you can't pull out of a high speed dive. The compression speed is different for every plane, and is known as it's "critical mach number"; the proportion of the speed of sound (mach number) at which the pilot is no longer in controlled flight. To make matters worse, other important factors, such as the centre of aerodynamic lift, move around a bit at these speeds too - A famous example is the P38 developing a strong nose down tendancy at about the same time the elevator stops working (you can imagine the result...)
It's important to realise that the speed of sound changes with altitude (air pressure); and so, as you dive lower, you're entering air where the compression threshold is higher. This is why you may lock up the controls on a P38 ar around 380 IAS at 20K; but 10K lower, if you're lucky, you might get control back at 400 IAS - the lower you are, the faster you can go without compressing.
Another famous example is early Typhoons - they could dive so fast they'd start to compress, get into lower, thicker air where the elevator would suddenly regain it's authority (it'd work again); and you suddenly had a pilot doing 500 IAS and yanking back hard on a stick which would suddenly work - he didn't just black out, he'd snap the tail right off, a weakness of the early Typhoons.
Think of all the Kamikazees you've seen in film of the pacific war *just* missing thier target. They're not dead (probably); they're compressed - they power dived a Zeke, which has a low critical mach number (means it compresses - locks up - at a relatively low airspeed), compressed - and now they can't "aim" the plane - so they auger right next to it......
Control authority (elevator, rudder etc) is just a formal way of saying the control works. If I understand Mandoble's reasoning here, he's asking two questions:
At what speed should the various airframes compress? (in otherwords, are the critical mach numbers for each airframe correctly applied)
At which speed thresholds should the symptoms of compression set in for each aircraft? (compression rarely happens all at once, the controls get heavy and the plane may start to shake and grumble) - If I understand him properly he's questioning at what speed should the Dora's stick get stiff (if at all).