If the distance between earth and moon were to be changed, at least two properties or phenomena would be affected: time it takes for light to reach from moon to earth and tidal heights.
If the distance between moon and earth was tripled, then the time taken by light to reach from moon to earth will also be tripled (since the velocity of light in vacuum is constant). It currently takes a bit more than a second for the light to reach earth from moon. Under new scenario, it would take 3 times as much time for the same.
The gravitational attraction of moon results in tides in earth's oceans. If the distance between moon and earth was 3 times the current value, moon's gravitational pull will be reduced by a factor of 9. This will result in lower tidal heights.
Hope this helps.