Other mistake: During the battle near the end of the episode, Sisko is heard saying, "Locking onto the lead ship" but he gives the firing order to Bashir, who is seated at the helm. This implies that the targeting controls and firing controls are at separate stations, which makes no sense.
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.
Other mistake: Sloan arrived at the station to destroy the cure, and he and Bashir discuss the fact Sloan has to know what it is to be able to find it in Bashir's lab to be able to get rid of it. Sloan counters he could destroy the whole lab, and Bashir dismisses this as not subtle enough for Sloan. Obviously they've both forgotten that Bashir has perfect memory, so he'd need to be killed to get rid of the cure as well, not just destroy the lab. Something which Bashir would have brought up to back his point up, or Sloan could have used to defend his idea, destroying the lab with Bashir inside, getting rid of both.
Other mistake: When Sisko was initially meeting and speaking with Kira, she described the station by calling it a, "Godforsaken place." From her perspective, she should have said, "Prophet-forsaken place." Also, later in the episode, Quark refers to the Bajorans as, "Godfearing people." Once again, should have been, "Prophet-fearing people."