A ritual is introduced of displaying emptied power cells from the phaser array in the Defiant's mess hall. Phasers draw power from a ship's energy grid. Giving them their own power cells that can run out and need replacing would be inefficient at best and dangerous at worst, as they could run out in the middle of a battle.
When O'Brien delivers the depleted power cell from the phaser array to the gathering of the crew he struggles with its weight. But when he passes it to Dax and she gives her speech, she doesn't struggle, but handles it as if it had hardly any weight at all. Also, when Dax puts the cell on the rack with the others, one of the cells it touches moves too much for something that is supposed to be quite heavy.
After Nog pours the brandy and picks up the tray to carry it back to Captain Sisko's table, the camera pans across the crowded mess hall. One officer in a blue science/medical uniform close to the camera is not wearing any rank insignia on his collar. Even enlisted crewmen, such as O'Brien, have some kind of rank insignia.
As Sisko finishes his conversation with Dax on the Defiant's bridge, and is about to walk out the open door, beginning at 25:46 red blocking tape in parallel lines is clearly seen on the floor outside, from the door angling down the corridor, which Sisko (Avery Brooks) then exits the scene walking in between the red lines as the actor is supposed to.