If the amount of light coming out of the interferometer is proportional to the gravitational wave signal, then the uncertainty in the gravity wave strength is just proportional to the statistical uncertainty in the number of photons that are arriving. This shot noise limit is the thing that drives us toward greater and greater laser powers. A factor of 100 greater laser power will improve gravity wave sensitivity by a factor of 10. That's the nature of shot noise. At such sensitivities, the internal thermal noise becomes important.
All masses have thermal noise due to the vibrations of the atoms.
All those shaking atoms cause the mirror surfaces to vibrate, an adverse effect when you're trying to sense where those mirror surfaces are. Then there is suspension thermal noise. The masses will be suspended on simple steel piano wire and any thermal noise there may affect the movement of the mirrors. Another problem is radiation pressure. As the photons hit the mirrors, they actually impart momentum to the mirrors and cause them to move.