Continuity mistake: At the end of the episode, Odo has sent everyone affected by the telepathic matrix to a cargo bay. Sisko and O'Brien remove their com badges, throwing them aside before heading to the bay. After everyone is cured, Sisko straightens back up and, in the closeup, you can see that he has a badge on. In the next closeup, its gone again.
Continuity mistake: When Dukat pours wine (in close-up) for himself and Adami, the glasses each contain very different amounts of wine as he puts the bottle down. But in the wider shot, he hands Adami her glass while holding his own, and both appear to have the same amount of wine.
Deliberate mistake: The dying Vantika hides his consciousness away in a portion of Dr. Bashir's mind. At one point, "Bashir" (heavily cloaked in clothing and shadows) comes up behind Quark and makes sure his demands are clear. At this point, it should still be unclear just how Vantika is still "alive", and whose body he is using. However, when he shoves Quark away, for a fraction of a second, Bashir's face can be seen under his hood. They were true to plot in using the right actor (though he shouldn't have been seen), it is possible some might have spied the secret earlier than the show meant to reveal it.
Continuity mistake: When Arissa is first interviewed in Odo's office, she displays a 'data port' that is embedded below and behind her left ear in her upper neck. Her hair is styled to make it visible, and the port seems to be there for the entire scene, tho almost completely obscured at times. The second time she's in Odo's office, her hair style is the same, making it very obvious the port has now vanished, and it's gone the entire scene. For the third visit to Odo's office, the port appears and disappears at random. Apparently this scene was comprised of shots from the two separate shoots that made up the first two office scenes.
Plot hole: Earlier in the season, it was established that the Jem'Hadar are genetically engineered to be loyal to the Changelings, meaning they will not deliberately harm them. With that in mind, the Changelings still care about Odo's well being despite his refusal to return to them. So why didn't the Lovok Changeling send a message to the Jem'Hadar ships to inform them that a Changeling was going to be on the runabout? Given that he took time to offer another chance to return to his people, you would think he'd take time to make sure he returned to the station safely.
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.
Continuity mistake: When the Breen fling Dax into the cell after interrogating her, she (the stunt woman) lands front-down, facing her left side, with her left knee raised. (To clarify her body position, if she were vertical, it would appear her left foot was resting on the seat of a chair) The camera angle changes instantly so that we see Worf rush to her side as he kneels on one knee. But that knee is on the ground exactly where Dax's knee should still be. But it isn't, because both her legs are suddenly straight.
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.
Character mistake: When Nedelle collapses, everyone looks to Jadzia to save her and she says she can't. Why do they think Jadzia can save her? She isn't a doctor, and the Dax symbiant was never a doctor either. They are on board a Federation ship, with a Federation crew, why do they not call the ship's doctor?