The matte paintings depicting a city in the episode Angel One (1988) are reused in this episode to show Klaestron IV. The painting of the city at night was modified to remove most of the leaves from a tree in the foreground, and a building with a dish on the roof was extended by several stories. However, the day matte painting was not altered, so the tree suddenly regrows its leaves and the building shrinks dramatically in a day.
At index 11:22 the reflection of a teleprompter screen is visible on the glass table in front of Sisko.
The hearing as a means to delay the extradition of Jadzia Dax in order to find evidence for her defense would be unnecessary. Even if the Klaestron IV representative was correct that they could conduct a "unilateral" extradition, the assault on Bashir would provide Sisko the right to hold their entire team for trial, rendering moot the need for the hearing since they could not transport Dax while in custody for assault.
It makes no sense that they'd shut Quark's bar - disrupting passengers at DS9 - and have a trial in public view of the Promenade. They could have easily used a holosuite and created an appropriate environment or just gone to Bajor. Although in reality this would have been a cost saving measure to use an existing set.
The Federation has a firm conviction against capital punishment, they are against it even for the worst types of murder. General Order 7 was the only capital crime the Federation ever had and even it was repealed by the turn of the 24th century. So it seems highly unlikely they would sign an extradition treaty with a government that still uses it. There are real life examples, countries like Canada and the United Kingdom will not extradite prisoners if they are facing the death penalty.
Assuming the Federation's extradition treaties work the same way real ones do Sisko had ample reason, besides the fact that DS9 is a Bajoran station, to deny the Klaestron's extradition request. Law enforcement officials cannot just go into another country that a treaty exists with and arrest a citizen of that country. A request for extradition must first be filed with the government where the person in question is a citizen of for it to be legal. From a legal standpoint if law enforcement arrests a citizen of another country on foreign soil where they have no jurisdiction and takes them back to their country by force they would be guilty of kidnapping in said foreign country. So both the Bajorans and the Federation would have every right to deny their request and to also charge the Klaestron's with attempted kidnapping.
Ilon Tandro being sent to arrest the person accused of murdering his father, plus him representing his government in the extradition hearing, is a major conflict of interest. Which is an argument Sisko should have made, especially since he recently removed Odo from an investigation due to a conflict of interest.
At one point, Sisko asks Jadzia, "The competition to become a Trill is very strong, then, among potential hosts." However, Jadzia was born a Trill, so Sisko should have said "joined Trill" instead.
Jadzia mispronounces "zoology," saying it as if it starts with "zoo," when the first syllable should actually rhyme with "toe."