I would imagine that stray shots are very unlikely to hit anyone who wasn't in the area with any kind of strength. Not only would you have diffusion of the beam, the energy of the beams would eventually be sapped by interstellar medium (remember, space isn't a total vacuum).
Also, referring to something you said earlier in the thread, Timo
, there's never been an instance I can think of where phasers fire FTL. In fact, they all seem to be slower than light, since in nearly all cases, there is a noticeable travel time in the beam (i.e. not visually instantaneous), which would explain why it is in fact possible for ships and people to dodge phaser attacks.