When firing a weapon like the phaser that is basically a "continuous stream" laser beam weapon, why fire it in short, brief bursts only (like a conventional cartridge firearm), as the Starfleet officers do during the battle? Firing in this manner allows the oncoming Jem'Hadar soldiers to dodge & duck the plasma bursts, and also gives them time between shots to find cover & return fire. Unfortunately, just like conventional weapons, phasers have a limited supply of ammunition (energy). If continual fire were used, their power packs would be drained too fast.
When Worf contacts Sisko from the Defiant the communications chirp is from Deep Space Nine's communication system and not a Starfleet system.
Either the "Houdini" mines come in a large variety of sizes, or there are problems with the perspective and placement of the CG mines.
Jem'Hadar are meant to be incredibly skilled warriors with strength and speed far beyond those of humans. They are even stronger and more ferocious than Klingons. Yet human Starfleet officers are shown repeatedly and easily besting Jem'Hadar soldiers in hand-to-hand combat.
Captain Sisko is informed only after he beams down to the planet that the captain and first officer of the Starfleet forces there had been killed days earlier. There is no reason this information would have been kept from Starfleet Command or Captain Sisko.
Ezri Dax is Deep Space Nine's station counselor. There is no reason for her to accompany the Defiant on a supply run. The Defiant is deployed only for short-term combat missions. Having a counselor onboard would serve no purpose. It makes even less sense that she would then beam down into the combat zone on the planet.
When Quark and Ezri are conversing in the mess hall, red alert sounds after the ship is rocked by Jem'Hadar fire. Red alert would have been called when entering a combat situation, not after the battle had already begun. As the Jem'Hadar ships do not having cloaking devices, the Defiant would have spotted them and raised red alert well before they were fired upon.
Dr. Bashir is shown armed and taking place in active combat action. Medical professionals are not supposed to do that, even during wartime. It violates his Hippocratic Oath. Most rules of engagement declare medical personnel off-limits as long as they are not armed or participating in combat. While the Jem'Hadar may not hold the same regard for medical professionals, Starfleet still does. For that matter, Ezri is part of Starfleet Medical (as she is a mental health professional) and should be excluded from combat operations, as well.
Captain Sisko makes the decision to remain behind on AR-558 and help reinforce the Starfleet crew that's been holding it. While this may seem on the surface like a brave and noble act, Sisko is the commander of the Ninth Fleet and one of the chief organizers of the Federation war effort. Putting himself at severe risk in order to show compassion to the 42 Starfleet officers stationed at AR-558 is foolish.
When relaying the events of the ambush that killed Lt. Larkin, Nog says, "There was all this phaser fire." Jem'Hadar do not use phasers, they use plasma rifles. Given his medical condition at the time, the mix-up is understandable.