From 1 AU (exactly 149,597,870,700 metres by official definition) the Moon, at its brightest would have a visual magnitude of 0. The Moon, contrary to its lyrical likening to silver, is quite dark, reflecting only 13.6% of the light falling on it. If it was a perfectly reflective sphere its magnitude would be about -2.1 at 1 AU. But 0 it is. Place it in an orbit of 3.1622 AU from the Sun and it’d be at magnitude +5 – visible to human eyes as a faint star.
At 10 AU from the Sun, the light we get back from it would be 1/10^4 = 1/10,000th and its magnitude would be +10. Human eyes can, given a dark sky, see down to about magnitude +6.5, so we’d need a telescope to see the Moon if it was orbiting Saturn.
If the Moon was at 31.622 AU its magnitude would be +15 and it’d be as challenging to see as Pluto. At 100 AU it’d be magnitude +20 and only large professional telescopes would see it. At 316.22 AU it’d drop to +25 and not be detected by Pan-STARRS with its +24 hoped for maximum. At 1,000 AU it’d drop to +30 and only be detected by the Hubble Space Telescope, which has captured objects down to +31.5. If it pointed in the right direction.
Beyond that distance, the main hope for detection would be via occultation – catching the object as it passes across a bright star in our field of view. Basically the same way that the Kepler mission sees the multitude of planets it has detected, though the obscuration would be total and non-repeating. To capture such an event requires watching millions of dim stars and galaxies, in the hope something much closer blocks it from view. Presently several different sky surveys might capture chance events further away in the Galaxy – for example if they stare towards the Galactic Core many millions of stars would be in view. A chance shading or two would tell us vital information about the numbers of interstellar planet-like objects. One estimate, based on a single event, suggests thousands of interstellar planets for every star.