In generally, I don't think the physics allow a moon to have a moon. The gravity of the planet would almost certainly win out in a tug of war.

Digging a bit more, my point about a tidally locked moon not having regular (oceanic) tides wasn't correct. Only if the orbit is circular will there be no tides. Any moon, tidally locked or not, that has an elliptical orbit would experience tides due to the difference in gravitational pull at different distances from the planet.

Of all the peculiarities of tidally locked moons, I believe the one that presents the most difficulty with respect to it being a "normal" (earth-like) planet, is the length of day. Assuming the moon orbits along a different plane than the planetary orbit around the sun (a very reasonable assumption/possibility), then you don't have to worry about it being "in the dark" any more than is thematically interesting. But you DO have to deal with the fact that the day/night cycle is likely to take between 2 and 20+ earth days.

Now if you're allowing magic, particularly planetary magic of the type previously proposed to replace/enhance the magnetosphere, then there's no reason you couldn't hand wave the physics in this one case and declare that the planet orbits quite close to the planet and only has say... a 28 hour day. Happy/interesting side effect: the planet would be frickin' HUGE in the nighttime (and probably daytime!) sky...