YES! Here are the explanations...
1. This must be fun... The crew must secretly be having a good time, especially Dax's comment of it being fun.
2. Power goes out accidentally... O'Brien pulls a component out causing the section of the Enterprise he is in to lose power.
3. Poetic justice... Darvin believes his plan to kill Kirk with a bomb implanted tribble is poetic justice.
4. Contours... Dax comments on nice design of 23rd century tricorders, specifically mentioning contours.
5. A person in their prime... Dax wanted to see Koloth in his prime.
6. A lie before is a lie again... When O'Brien lies to Kirk, it is the second time it was done, as the first time is in the original episode with another crewman saying the same lie.
7. An important clue... Bashir sarcastically mentions the raktajino clue when Odo mentions it and how others would have missed it.
8. Unexpected taste... Sisko thought Dax was salivating over Kirk, but it was really Spock.
9. Four there, two there... Sisko, Dax, Bashir, and O'Brien are on the Enterprise, while Odo and Worf are on K-7.
10. A confusing change...Bashir, O'Brien, and Odo are confused as to why the other Klingons don't look like Worf.
11. Interesting theories... Bashir and O'Brien come up with theories for the difference in Klingon looks. (ENTERPRISE showed they were both right.)
12. Admiring the eyes... Dax loves Spock's eyes.
13. They have seen this ship before... The crew recognizes the Enterprise.
14. A Lt., not a captain... Sisko poses as a Lt., as he felt wearing any higher rank was pushing their luck.
15. Not a historian... Bashir uses the McCoyism here.
Your turn, Prax.