In no particular order...
Duet: When "Gul Darheel" is talking about what a contemptible coward Amin Mirizha is and he breaks character and breaks down.
The Most Toys: When Data makes the decision to kill Kivas Fajo and then lies about it (and thank you to David Mack for coming to the same conclusion that I did, that Data has always had emotions).
Past Tense: Both parts just the horrifying situation that many of those people are in, and how closely it parallels things today.
Also towards the end of DS9 when Garak's mother dies.