Yep same issue here. Engine afterglow and trails all way off to the left side of my ship and the blinking lights are under it. My weapons and some other activated abilities graphics are firing off from right side of ship. All from empty space.
There's a few of us on a different thread who are having the same issue. Sounds like it erupted after a recent patch, else we'd be seeing alot more about it. I think those that have the ship but don't fly it so much (or at all anymore) should jump back in and see if theirs is now suffering from the same problem.
Most of the Draguas's out there, I presume, are shelved after having the console stripped...but some of us actually want to fly it! And for 1500zp, it's prudent that Cryptic address this.
My player's Draguas is fine but all of the NPC Draguas' I've run in to have the bug. I wonder if the ship model has been updated to the newly added NPC version, and since I had mine previously it's fine. I'm not about to go change things in the shipyard though. Maybe I'll try on the Tribble server.