Disinfectants like calcium hypochlorite actually become more effective at killing hot tub bacteria as the pH goes down, so an acidic pH will not hamper disinfection initially. The lifespan of the chlorine in the hot tub will decrease, however, because you lose chlorine to outgassing and degradation more rapidly at an acidic pH. Over time, chlorine levels in your hot tub will drop more rapidly. This effect is accentuated because the warm temperatures in your hot tub accelerate the breakdown of the chlorine in any case.
Low, or acidic, pH accelerates corrosion of metals like the pipes and equipment in your hot tub. Again, the temperature of the hot tub water accentuates the problem, because higher temperature accelerates chemical reactions like those that drive corrosion. This effect is especially undesirable because it shortens the lifespan of your equipment and may eventually necessitate costly repair or parts replacement.
Calcium carbonate becomes increasingly soluble at acidic pH levels. A common experiment in grade school involves placing a piece of limestone in hydrochloric acid; the limestone fizzles and reacts to form calcium chloride and carbon dioxide gas. The results in your hot tub are not quite so dramatic; nonetheless, a lower pH will retard scale formation. If the walls of your hot tub are made of calcium carbonate or similar materials, you will accelerate the rate at which they dissolve.
A pH level below 7 may irritate your guests' eyes and skin, and the lower the pH drops, the more pronounced this effect will become. The ideal range for pH in your hot tub lies between 7.2 and 7.8, a pH level that promotes disinfection while avoiding the deleterious consequences of an over-acidic pH. Testing your hot tub pH frequently and correcting as necessary will help you avoid these kinds of problems.