At one point when talking to Tendi about his apprehension toward working on the royal cruiser, both sides of Rutherford's head are colored solid gray like his cranial implant. Only the left side of his head has the cranial implant. When he turns his head again, the right side of his head is once again colored the black of his hair with the two lines shaved into it.
Boimler is seen in his bunk polishing a phaser rifle. Ordinance aboard a starship is tightly regulated. An officer would not be free to take a rifle back to their living space.
Bullips says that "a life of high adventure can't compare to working on the old impulse engine." As he says this, he points to the warp core.
Tendi tells Rutherford he should "definitely learn how to curtsy" when going aboard the royal cruiser. Curtsying is done when wearing a dress. Rutherford does not wear a dress.
Boimler says he used to do wetwork all the time when he was on the USS Titan. Wetwork is a euphemism for murder or assassination. It's very doubtful that a Federation/Starfleet ship would do such a mission.