Billups calls Rutherford his "number-one- with-a-bullet systems guy." In the previous episode, Rutherford's conversation with Ensign Barnes established that he and Billups were not well acquainted.
After the bar brawl, Boimler has two shards in his leg. Mariner pulls one out, then rubs together some plants to make a numbing agent for Boimler's leg wound. When she applies the agent, both the shards are gone. After she finishes rubbing it on, both the leaves and the wound have disappeared. A numbing agent would not make a wound disappear. Further complicating the matter, in the subsequent wide shot, the leg wound is back, though no longer bloody and the leaves are still gone.
Rutherford's cranial implant is shown to be able to develop combat strategies and help him execute them. However, many of the feats he engages in would require superhuman ability not accounted for by simply having good strategy. He is punched by Borg and punches Borg but receives no wounds on his face or hands. He is able to rip metal bars out of the combat ring and tear off Borg limbs with his bare hands.
Boimler wonders where K'orin and Mariner got flagons of bloodwine on the shuttle. Starfleet shuttles are equipped with replicators, so they could have very easily replicated the bloodwine. However, it is correct that replicators cannot create living matter, so K'orin would in fact need to go to the Klingon district to obtain gagh.
Boimler brushes up on his formal Klingon greetings before meeting K'orin. The Federation and Klingon Empire both use universal translators. Whatever Boimler says, K'orin will hear it as Klingonese, regardless.