It's mentioned that the top speed of the USS Prometheus has been increased to warp 9.5 so that they can escape if the experiment goes wrong and causes a supernova. But even a supernova can't exceed the speed of light, so they would be able to escape at warp 1.
Seyetik refers to a recipe being cooked "at exactly 500 degrees Kelvin". Kelvin is an absolute temperature scale and is not measured in degrees. The proper unit is simply Kelvin.
The commanding officer of the USS Prometheus wears the rank insignia of a lieutenant junior grade. Such a low-ranking officer would never be given command of a Nebula-class ship, or any Starfleet vessel.
It's quoted prior by Sisko that the ''Fall of Kang'' is required reading at the academy. Yet the officer on Seyetik's ship doesn't know it, ''What is he talking about?''
When the senior staff is having dinner aboard the Prometheus, Commander Sisko's rank insignia are crooked.
When Nidell is apparently dying, Dax is the only person attending to her. As they are on a Federation starship, there should be a full medical staff.
When explaining a recipe to Chief O'Brien, Dr. Seyetik says it must be cooked at "exactly 500 degrees kelvin." Unlike Celsius and Fahrenheit, the Kelvin temperature scale does not use degrees in its nomenclature. It would be properly stated as "500 kelvins," not "500 degrees kelvin." A man of science would be keenly aware of this and not make such a rudimentary mistake.
After Seyetik's death, Nidell finds Sisko on the Prominade. He asks how she found him. But he's wearing his comm badge, which can be located by computers just by asking. This process was first demonstrated on StarFleet ships, but has been shown to be a part of the Cardassian computers' functionality too.