Here's the thing about cloaking device continuity: The only thing that makes sense is if there are several completely different cloaking technologies. Think about it. Chronologically:
In Enterprise, the Suliban and Romulans used a form of stealth technology that Starfleet learned how to penetrate with sensors obtained from Daniels. The Xyrillians also had a form of invisibility for their ships. Yet:
In TOS: "Balance of Terror," the technology to cloak a ship from sensors was considered prohibitively impractical, until it was achieved by the Romulans. Yet a cloaked ship could still be detected by motion sensors. However:
In "The Enterprise Incident," cloaked ships could no longer be detected by motion sensors. Starfleet stole a cloaking device, presumably with the intent of learning how to reproduce and/or penetrate its effect. Yet:
In TAS: "The Time Trap," Klingons were known to have cloaking devices, though nothing was established about how they worked. By The Search for Spock, they were still using cloaks, but those cloaks could be detected by a visual distortion effect. However:
In The Undiscovered Country, a new form of Klingon cloak was undetectable by the distortion effect. Spock discovered how to track a cloaked ship using its engine emissions. Nonetheless:
By TNG, Starfleet has no ability to track cloaked ships by engine emissions.
The only explanation that makes sense is that there's a constant war between stealth and detection. Once a given form of cloaking technology is penetrated by a new detection technology, it becomes obsolete and useless until a new form of cloak is invented that can fool that detection technology. Cloaking devices are not a single invention, they're a whole string of successive inventions. And an obsolete cloaking technology might as well be no cloaking technology at all.
So there's really no continuity error here, any more than there is among all the other examples cited above. The explanation is that the cloaking technology used by the Alliance in "Crossover" has been penetrated by Rebellion sensors in the interim, thus requiring the Alliance to obtain a new, more advanced form of cloaking.
