This problem can be detected by measuring total dissolved gases (DO, nitrogen, argon, dissolved carbon dioxide etc.) though the equipment required is expensive.

Gas bubble disease is supersaturating of gases  in the water due to pumping under pressure and/or cold water heating up to room temperature. Tap water distribution systems are maintained under pressure at all times, both to insure adequate flow and to prevent polluted water from outside the pipes to enter in at leaks. Any additional gas introduced into these pipes (e.g., a leaky manifold) will be dissolved at these higher partial pressures, and will often be supersaturated when it emerges from the tap.

Also, gases are more soluble in cold water than warm, so when gas-saturated cold water emerges from the tap and warms up in an aquarium, the water becomes supersaturated and can form bubbles. The problem resulting from this phenomenon is called gas-bubble disease.

This is characterized by the formation of gas bubbles in the body cavities of fish, such as behind the eyes (causing exophthalmia) or between layers of skin tissue. Typical signs of which are visible air bubbles in the eyes, gills and sometimes in the skin. Small bubbles can form within the vascular system, blocking the flow of blood and causing tissue death. Worse, bubbles can form in the gill lamellae and block blood flow, occasionally resulting in death by asphyxiation. At 140% saturation and higher, gas bubble disease can cause fish kills, although the effect can cause some problems at 105-140% saturation.

Stirring up bubbles during a water change doesn't hurt your fish, but it probably doesn't do much for them, either. It may hasten the degassing a bit, but you certainly aren't removing chlorine/chloramines by this method.