I believe this idea is in progress by the devs. The team has already stated they will improve effects and add them to weapon effects. However, the details are limited at this time, so this would be a great thread to gather ideas on how various weapon effects might look. Bring on the pictures!
I'll get it started:
The point where a beam hits something should probably spawn some kind of flash image billboard to simulate a "bloom".
Similarly, I'd like it if damaged, exposed system blocks, especially power blocks, were to spawn a client-side particle and eject it away from the ship's center every once in a while to simulate some kind of leak or ongoing "fire".