EF: There is a train station in Wales with a name almost as long as that sentence
Basically lasers go on forever, until every last wave of light has hit some tiny particle somewhere in space. Stars can be seen clearly several thousand light years away and their light is not even coherent, even if they ARE very very bright. My guesstimate would be that your laser could be picked up by extremely extremely responsive gear (which could measure every single photon) a couple of planets away.
Now Eku has answered pretty well about the visibility already. A laser is always brighter seen from the recipient's point of view, and if that person was standing in total darkness your 100mW would probably be visible about 5km away.
I think this part has been answered way better some other place on LPF and it is difficult to say what a "visible" laser is.. whether the mere fact that you can sense some change in light is enough or that you need to see a clear beam coming towards you for it to be "visible".
Anyway you should never ever shine at or near an aircraft, no matter how dim you think the laser is. You cannot estimate the hight of the plane well enough and cannot estimate how much light is visible at that distance. Pilot's eyes are also adjusted to very sensitive night vision with very dim control boards in the cockpit and so on, and a tiny flash from a laser might be enough to distract them and cause them to report your laser, or in the worst case cause an accident.
Also pilots often stray from their planned flight path (I should know, about 10 fly straight over my house every day even though their route is listed as 8 miles away!) and it is therefore even more difficult to estimate hight and location of planes. Just don't shine it at planes. Ever.
Another interesting thing observed by many here on the forum, including me, is that the longer the wavelength (eg. red 650nm), the further the beam seems to extend into the night sky, while shorter wavelengths seem to create a fatter and more visible beam close up, especially blu-ray 405nm which can appear as thick as a baseball bat at just 10 yards distance.
My theory on this is that it is caused by short wavelengths moving up and down more and therefore encountering more particles to light up, while long wavelengths move less and therefore do not encounter that many particles so the beam is still not weak at a distance.