Continuity mistake: It's surprising that Joseph Sisko is still alive at this point in the series. In previous episodes, Ben seemed to imply his father was deceased. In "Emissary" and "Paradise", he said his father WAS a gourmet chef (which is still his current occupation in this episode). And in a conversation with Odo in "The Alternate", Ben told him of how his father had a severe illness that made him very weak and he was unable to help him in the end.
Character mistake: During the Defiant's flight to save the Cardassian officials, Worf says something to the effect of, "I've never been aboard a Federation ship equipped with a cloak before". However, he was aboard the Enterprise during the Pegasus incident, where the ship was temporarily equipped with a cloaking device.
Other mistake: Shortly after Quark, Rom and Nog arrive on Earth in the 20th century, just after they are observed through the one-way glass by the Army officers, the Captain in the hat who enters the room with the man in the suit to interrogate the Ferengi is wearing his rank bars on his shirt collar horizontally, parallel to his collar. The two bars of an Army Captain's rank should be worn vertically.