Zek tells Quark that the Alliance will release him only if Quark can secure a ship's cloaking device, claiming that they don't have cloaking technology in the Mirror Universe. This is inconsistent with what is shown in several previous Mirror Universe visits, where we see both Klingon and Cardassian ships with cloaking devices.
Rom refers to the fried tube grubs on Brunt's ship as delicious. It has been previously established that Ferengi eat tube grubs live and derive a good part of their enjoyment of the consumption of tube grubs from the sensation of them wriggling on the way down, even deriding those who suggest cooking them.
However, service tube grubs fried may simply be one of the differences exhibited by the mirror Ferengi. And Rom has often diverged from Ferengi norms in his tastes and behaviors.
When Worf rips out his captain's chair, he hits the console next to it, which wobbles, revealing that is is not solid metal but a poorly-secured prop.
The mirror counterpart to the Defiant can be seen with Starfleet markings on it in numerous shots. There is no Starfleet in the mirror universe. The hull markings are a result of reusing stock footage of and the same model as the prime universe Defiant.
As Quark and Rom are carrying the invisible cloaking device through the corridors, Quark's hands are clenched fists which wouldn't allow him to carry a device as heavy as a cloaking device.
Once Rom has finished installing the cloaking device on the Regent's ship, mirror Garak pushes him aside and says, "I'll take over from here." Garak has never used the cloaking device before. No one in their universe has. It's a specialized piece of equipment that requires training to use, as established in episodes such as "The Search" and "Once More Unto the Breach."
Rom complains that the universe is supposed to be alternate, but is in some ways similar, and therefore not "alternate." Alternate just means different, not necessarily completely the opposite.
Rom declares the mirror Brunt to be a "nice guy" and completely the opposite of their Brunt. However, mirror Brunt still does jobs for the evil Alliance.