New space travelers ask, "What does it look like outside a ship moving faster-than-light speed?" Part of the answer can be seen in a simple pane of glass. Light travels slower through glass than it does through open air; light also moves slower in conventional space than it does in a high-speed mass effect field. This causes refraction - any light entering at an angle is bent and separated into a spectrum. Objects outside the ship will appear refracted. The greater the difference between the objective (exterior) and subjective (interior) speeds of light, the greater the refraction.
As the subjective speed of light is raised within the field, objects outside will appear to red-shift, eventually becoming visible only to radio telescope antennae. High-energy electromagnetic1 sources normally hidden to the eye become visible in the high blue spectrum. As the speed of light continues to be raised, x-ray, gamma ray, and eventually cosmic ray sources become visible. Stars will be replaced by pulsars1, the accretion discs1 of black holes1, quasars1, and gamma ray bursts1.
To an outside observer, a ship within a mass effect drive envelope appears blue-shifted. If within a field that allows travel at twice the speed of light, any radiation it emits has twice the energy as normal. If the ship is in a field of about 200 times light speed, it radiates visible light as x-rays and gamma rays, and the infrared heat from the hull is blue-shifted up into the visible spectrum or higher.
Ships moving at FTL are visible at great distances, though their signature will only propagate at the speed of light.