In the US at least (probably most other places too), aircraft are tracked pretty accurately, so if you know the time it happened and the pilot can give a rough bearing, some triangulation should be possible. Add to that the fact that the area around airports (where such lasering usually occurs) is usually sparsely populated due to people not wanting to live near and airport, and it’s easy to see how it might be possible to narrow it down to a specific address.
One thing about a powerful laser is that it scatters off of dust particles and anything else in the air, including the air itself (Rayleigh scattering). As a result it should produce a faint line in the air that points back to the source.
