Amplifiers sold in the U.S. are subject to the FTC regulations as to power claims and have to report the results after 5 minutes of continuous operation at the maximum power rating. The frequencies covered and maximum distortion level also must be included. Somewhat ironically, this is the only area of audio which is subject to relatively specific legal regulations, yet is often subject to suspicion by some who accept audible differences being present in even pieces of connecting wire.
When tested by the manufacturer and by independent testers, who almost uniformly verify the accuracy of the manufacturer's specs, the points you mention relating to frequency response, noise and distortion all are part of the procedure. All are typically at a level which allows for transparent amplification, with the incoming voltage simply being increased to make it enough to drive speakers at loud listening levels.
