How does movement affect potential communication with aliens?

We see depictions of our solar system that are not drawn to scale with the planets all nice and neat in a row. But that's not the way it is. All eight planets are never in a row, and vast distances separate them. Not only that, but they are constantly in motion.

We sort of assume that our sun is stationary in space. But that's not the way it is. The sun is moving at incredible speed around the galaxy and taking with it you and me and Earth and all the other planets and the dwarf planets and the asteroids and comets, etc.

The stars look static in our sky. In the northern hemisphere they rotate around what we call the North Star, but their positions relative to each other do not seem to change. But that's not the way it is. All of the stars are in motion, but because we view them from unimaginable distances the movement is not evident in a human lifetime. Given enough time, the Big Dipper will no longer look like a dipper when viewed from Earth.

We sort of assume that our galaxy is stationary in space. But that's not the way it is. The Milky Way is also moving at incredible speed as a vast conglomeration of stars and other objects.

Wouldn't all this movement impact on interstellar communication?

Take, for instance, the WOW signal that was detected in 1977. Since everything in the cosmos is in motion, isn't it possible that Earth just happened to be for a brief moment in the line of an alien signal? And that the signal could not be detected afterwards because both we as the recipients and they (whoever they are) as the senders had both moved?

This may be compared to driving past a low-watt radio transmitter. For a few minutes you may get the signal loud and clear, but if you keep driving it will invaribly fade.

Perhaps if everything stopped moving then detecting alien signals would be more likely. But that's not the way the universe works. Is all that movement sabotaging our efforts to hear from ET?