My NX-class displays the same graphical error on the bridge dome. It's been that way since Season 4 released. I've submitted a bug report at that time. But I couldn't tell you the number. I visited the Shipyard and messed with the costume a bit as recently as this weekend. But the dome remains unchanged.
What I haven't tried is dismissing the starship to reclaim/purchase a new copy from the Shipyard. I don't know if that would be a different experience or not.