Ben Sisko discusses Joseph Sisko's health with him, based on information he received from Joseph's doctor. Doctor/patient confidentiality would prevent discussing those sorts of details with a third party, even if that third party is the patient's child.
Worf orders the computer to replay the footage of the conference explosion at 1/10 speed. The actual playback is not that slow, closer to 1/2 speed than 1/10.
Mis-pronunciation of boudin as 'boo-deen'.
Also should be crawfish, not crayfish.
Also should be crawfish, not crayfish.
During the scene where Jadzia Dax is putting Odo's furniture back into place, Odo tells her on two separate occasions to "move it to the left," when she clearly moves it to the right.
Joseph Sisko says he has a pot of crayfish, but says "cray fish." A New Orleans native, even in the future, would have pronounced the word with the Southern dialect, "craw fish".
Worf states that the Klingons' gods are dead and ancient Klingon warriors slew them "a millennia" ago. "Millennia" is plural; the singular is "millennium". Additionally, a later episode elaborates on this mythical event, in which the first Klingon man and woman destroyed the gods shortly after being created. Presumably, Klingons don't believe that they have existed only since the 14th century.
Jake contacts Captain Sisko and tells him that "grandpa's been arrested." Joseph Sisko has not been arrested, he is simply not complying with an order to submit to a blood test. He has not been detained or taken into custody.