Like Scorpion, this is a two-parter that had a lot of work to get to the screen.
The original plan was that the Obsidian Order wanted Garak dead after he killed Entek in Second Skin, and he'd blow up his shop to draw Odo into an investigation and therefore uncover the assassination plot. Then, they dropped the link to Second Skin and instead looked at the episode as a sequel to Defiant, which would reveal what the Order was up to in the Orias system. But that was eventually rejected in favour of the plot as seen on TV.
After this, the show was originally planned to be a single episode, but instead of joining Tain on his mission to the Delta Quadrant, Garak would have told Bashir to give an isolinear rod to Sisko (instead of joking that he should eat it), and Garak would use it's existence to blackmail Tain into letting him and Odo go. This was felt to be too weak, and the episode was switched to being a two-parter.
However, this choice was made quite late in production, so Through the Looking Glass (the mirror universe episode) was already in production. As a result it was shot in between Improbably Cause and The Die is Cast, though it aired before the two-parter.
A few firsts: This is the first two-parter in Trek history have different names for the two episodes; it's also the first two-parter to be directed by a series regular (Avery Brooks directing Improbable Cause, in this case). The Search, Part II and Past Tense, Part II were directed by Jonathan Frakes, but he, of course wasn't a regular on DS9. It ws the first appearance of Mila, and the first appearance of a redesigned Tal Shiar uniform - Ron Moore hated the old one.
In a last, this is the final episode in which Avery Brooks does not sport a beard.
Behind the scenes, The Die is Cast is the first episode with Ira Stephen Behr as Executive Producer, who wanted to shake the show up - he especially wanted more space battles, and to show those battles as opposed to TNG's standard where most of the battle is described by the crew. To that end, the battle in The Die is Cast is the biggest seen in Star Trek to date. The motion control photography took 20 days to complete, a record for a one-hour TV show. 4 days of that was just for the shot of Defiant flying through an exploding Jem'Hadar fighter.
To keep the budget down, most of the Cardassian and Romulan ships seen in the episode are transparencies of the models, filmed in the background of other effects shots. Gary Hutzel made sure the camera didn't linger on them for any length of time, to hide the effect.
Some continuity notes: This is Commander Eddington's second appearance, and his betrayal of Sisko foreshadows his eventual betrayal of all of Starfleet when he's revealed to be a Maquis sympathiser. As we later learn, Tain does not die here, but becomes a prisoner of The Dominon. The aftermath of the Obsidian Order's failure leads to the downfall of Cardassian Central Command and the rise of the Detapa Council, just in time for Cardassia to be invaded by the Klingons in The Way of the Warrior.
Admiral Toddman is the only Starfleet flag officer seen in any TNG-era production to not wear a red uniform. He jokes about promoting Sisko in their final conversation, but Sisko is indeed promoted to Captain 5 episodes later. Toddman was played by Leon Russom, who also played CinC Starfleet in Star Trek VI
The Changeling posing as Colonel Lovok infers that the Dominion has plans in place for the Federation and the Klingons, these would be explored in series 4 and early into series 5.
And opinion time:
While I really like this two-parter, I found part one to be a bit too much setup - there's false starts, a lot of back and forth, and it's quite convoluted. Which is suitable for a Garak episode, I suppose, but still. It's something of a casualty of the shift two a two-parter, especially as the second episode has all the meat, so to speak.
And that second episode is a tour de force, Garak has great scenes with Odo and Tain specifically, showing Andrew Robinson's range and talent, especially when he's wearing a ton of makeup. The barely suppressed glee and sense of release Garak has when chatting with Tain is fantastic, a side of Garak we've never seen as he's always so guarded in the station.
The torture scene between Garak and Odo is especially powerful because of everyone in the show at this point, only they can't go home. Garak usually plays his cards close to his chest, but it's clear that a return to Cardassia is a heart-felt desire. He doesn't want to torture Odo, but he'll do it if it means redemption in the eyes of his people and his father - and a chance to get even with Dukat and everyone else who wronged or escaped him. By comparison we were under the impression that Odo had utterly rejected his people, but it's only in the moment of his greatest desperation he reveals that he wants the same.
And yet, when the Changeling spy offers Odo a way home, he's turned down. Earlier in the story, Garak says that Odo is motivated by a sense of justice, and that rings true here. Odo's loyalty to his - I'm reluctant to say friends yet - companions on Deep Space 9, and his horror at the Dominion mean that even though he wants to go home, he can't. This internal conflict will come back to haunt Odo again and again as the story progresses, it's one of the best character arcs the show has.