Ascended Fanboy/The Knights Who Say Squee: Dax may be the most outwardly enthusiastic, but don't let that fool you. The other Starfleet officers are just as thrilled to be there and to see Kirk in action.
Sisko: Excuse me, Captain. Here's tomorrow's duty roster for your approval. Kirk: Lieutenant... uh, Lieutenant– Sisko: Benjamin Sisko, sir. I've been on temporary assignment here. Before I leave I just want to say... it's been an honor serving with you, sir. Kirk: All right, Lieutenant. Carry on. Sisko: Thank you, sir.
O'Brien stands in line, as Kirk dresses down the brawl.
"I lied to Captain Kirk! I wish Keiko could have been there to see it."
Author Avatar: Dax's enthusiasm for the time period of the original series was a direct reflection of the writers' love for the old show.
Bar Brawl: One of the most famous scenes in both tribble episodes. This time, O'Brien and Bashir get mixed up in it.
Scotty's "Air Punch" against one of the Klingons gets edited out.
Brick Joke: Odo buys a Tribble from Cyrano Jones, clearly not knowing anything about it. At the end of the episode, the Promenade is swarming with Tribbles. Makes his question about whether or not Sisko told Dulmer and Lucsly about the Tribbles a case of Fridge Brilliance, since it was his fault.
Call Back: This site doesn't have the server space to list all the references to TOS in this episode.
The Charmer: Averted. At one point Kirk glances over at Dax and she smiles at him. This was all the interaction they could show given what they had to work with, and they deliberately kept it as brief as possible to explain why Kirk didn't go over to talk to her (as one would normally expect him to do with an attractive woman like her).
Besides, Kirk was already occupied by the Tribble he'd just sat on, as well as all the other Tribbles swarming the bridge.
Continuity Drift: Dax recognizes Bones McCoy because she had met him as Emony even before he became a doctor and also sees Spock in real for the first time. Later in the series, we learn that she was implied as Curzon in Kithomer accords.
Deadpan Snarker: Odo, when questioning Worf about the Klingons' history with the tribbles, is particularly merciless with the sarcasm.
"Oh, another glorious chapter in Klingon history. Tell me, do they still sing songs of 'The Great Tribble Hunt?'"
Dax gets into the act while showing off the 23rd century miniskirt.
Future Imperfect: A mild, internal example, with some of the DS9 crew not knowing things about this era, such as the Starfleet division colours being different and what Captain Kirk looks like.
Grandfather Paradox: Lampshaded when Bashir encounters a woman he finds attractive who has the same name as his great-grandmother. He starts panicking over the possibility that he is his own great-grandfather and that he could cease to exist otherwise, but O'Brien tells him he's being ridiculous.
Bashir: I can't wait to get back to Deep Space Nine and see your face when you find out that I never existed!
Hand Wave: Upon seeing 23rd century Klingons, the crew asks Worf about the ridges.
Obstructive Bureaucrats: Played with. Temporal Investigations is apparently seen by most Starfleet personnel as people who show up just to make life hell for anyone who time travels, but the two we meet are pretty reasonable guys.
Oh Crap: Worf's reaction when he sees Odo's pet Tribble. Odo, of course, takes the opportunity to needle him about it.
Retraux: For the scenes in the past, the production crew intentionally used primitive equipment and lighting techniques to make the footage "mesh" with the original episode's.
Real Life Writes the Plot: Ira Steven Behr has said that the episode's premise was chosen because actor Charlie Brill, who played Arne Darvin, happened to come into the restaurant where the DS9 production crew was discussing different TOS homage-possibilities.