Revealing mistake: When he's attacked in Down Below, Dr. Franklin is shoved against a station bulkhead/wall that wobbles when he hits it. (00:15:30)
The Parliament of Dreams - S1-E6
Revealing mistake: As Lennier is first setting foot on the station, the same extra rides the escalator in the background up twice, even though we never saw him (nor was there time for him to) come down.
And the Sky Full of Stars - S1-E9
Revealing mistake: Inside Sinclair's mind, just after the knight shoots the fake Garibaldi, he lowers his gun and the end briefly lights up red. Evidently the actor accidentally pulled the trigger on the prop and triggered the light that lets the CGI team time the effects correctly. Note that it is not the gun barrel glowing after shooting, as it is not lit up before he lowers it.
Chosen answer: It was a piece composed expressly for the episode by Christopher Franke, who simply called it "Bar Background Music."
Jean G