As in many movies and TV shows, in the beginning when they show the result of the Breen's attack on Earth, it erroneously shows the Golden Gate Bridge heavily damaged, including the roadway and the main suspension cables severed. Due to simple physics, if the main cables are severed, the entire roadway and cables would collapse into the water, not simply hang in mid-air.
Sisko orders Worf to fire quantum torpedoes, which he acknowledges. The Defiant is then seen firing its pulse phaser cannons, not its quantum torpedoes.
The Defiant is equipped with ablative armor hull plating that can physically protect it against heavy attacks even without shields. Once its shields are disabled by the Breen here, the Defiant takes damage inconsistent with the function of the ablative plating.
At the 42 minute and 18 second mark in this episode, Jeffrey Combs's character, Weyoun, is seen watching a view screen. As the camera pans across the room to settle on Combs, he's wearing a different shirt. A much shorter and lower neckline reveals the lack of makeup which gives his race their pale complexion. The lower part of his neck and top of his chest are clearly visible and in his natural skin color.
Propmakers often have difficulties making old manuscripts convincingly, and the dangerous Kosst Amojan text Kai Winn reads to discover how to release the Pah-Wraiths has a common problem: its leaves clearly have printed paper pasted onto them, with the edges loose and visible, rather than text being printed or written directly onto the leaves. This process is much easier than printing directly on to the irregularly-shaped book leaves before binding them.
Worf and Ezri arrive at the station after being missing for about a week. Only Julian and O'Brien are there to meet them, and only in the capacity of welcoming them back as friends. Despite being chief medical officer of the station and knowing that the two were held captive and interrogated, Julian makes no mention of a physical examination to determine their well-being or fitness for duty (Sisko later requests it). Sisko casually wanders in late, asking about the Dominion/Breen alliance, but does not insist on a formal debriefing or report to Starfleet Intelligence. At the very least, as returned prisoners, there should have been more of a to-do about their arrival on the station than just two friends standing in a corridor.
The Breen do not possess cloaking technology, nor do the Dominion of the Cardassians. It is not explained how a contingent of Breen warships was able to make it to Earth unopposed.
The the battle at Chin'taka, the Breen wait until a number of their ships have been destroyed before deploying their energy-dampening weapons.
The Breen are shown at the battle of Chin'taka to possess energy-dampening weapons that can disable starships with ease. They did not use these weapons when attacking Earth. The Breen fleet that attacked Earth was almost completely destroyed. Had they used the weapons then, they would not have suffered such terrible losses.
Admiral Ross comes to Ben Sisko's quarters to tell him that the Breen forces have broken through Starfleet's lines in the Chin'toka system. If time is of the essence, it would have made more sense for Ross to contact Sisko over comms. Since Ross was not seen earlier and doesn't even have a permanent office on the station, it's not unreasonable to presume he had to travel there in order to speak with Sisko in person, wasting even more valuable time. Even if he was already on DS9 for some unknown reason, it makes no sense for him to walk to Sisko's quarters.
Weyoun suggests that Damar thought he'd "backed the wrong horse" in siding with the Dominion. Damar did not choose to side with the Dominion, Dukat did. Damar was elevated to his leadership status when Dukat had a mental breakdown, but he was not involved in the decision to form an alliance with the Dominion in the first place.
Kai Winn repeatedly refers to Dukat, in his identity as Anjohl Tennan, as "Anjohl." In Bajoran culture, the family name comes first and the given name is second. She should be calling him by his given name, Tennan.
The Female Changeling insists on going to the front lines for the battle at Chin'taka so that she may personally witness the Dominon/Breen alliance's victory. She is then not seen wearing one of the command headsets during or after the battle. As Jem'Hadar fighters are not equipped with viewscreens, without a headset she would be unable to see what's going on outside the ship.