Earthquakes
A habitable moon of a gas giant would have to have settled into the standard "one face toward the primary" rotation rate, like our Moon, for tidal forces to quiet down to the point where the place would be livable. The orbital period of the moon would dictate the day/night cycle (not counting enormous eclipses), but it would be hard to imagine that this cycle would be less than a week (similar to Ganymede's orbit) without getting into an uncomfortable radiation zone.
It would be interesting to see how a gas giant would behave in the hotter inner areas of a solar system.