first, the romulans having cloaking devices in the 22nd when they weren't supposed to have been first encountered by humans until the 23rd century (romulans had no cloak before Balance of Terror according to that episode).
That's not a problem. Cloaks have been penetrated and reinvented multiple times in the franchise -- e.g. in TUC Spock figured out how to track a cloaked ship by its exhaust, but by TNG that method no longer worked. It's just common sense that there'd be a constant arms race between stealth and detection, that there's not just one cloaking technology but multiple separate ones based on different principles. It's easy enough to surmise that the cloaking tech seen in the 22nd century was just some kind of holographic camouflage that Starfleet was able to penetrate and that fell out of use, and that the cloak in "Balance of Terror" was a new breakthrough in "true" invisibility of a type that had been deemed impractical.
the second time was in season 3 when the enterprise redefined warp coils from being the gigantic supermagnetic rings in the nacelles into a smaller portable device, much like the borg transwarp coil in Dark Frontier.
That's no worse than "Dead Stop" redefining "warp plasma" as some kind of fuel that could be stored in drums, rather than the superhot post-annihilation particle stream flowing from the reactor to the warp coils. And no worse than a lot of the sloppy technobabble in
Voyager before it. And at least in this case it can be justified by production necessities, in that it would've been too expensive to show them removing a massive structure from the other ship's engines and installing it in
Enterprise's nacelle, so they had to make it an affordably small handheld unit.
Really, Spock's dialogue in "Balance of Terror" was to inform the audience at home (long before it became a standard scifi trope) that there is some scientific theory behind the seeming magic of invisible spaceships.
Invisibility was a standard science fiction trope since at least 1897, thanks to H.G. Wells. (Actually the first story about a person being made invisible by science was probably Edward Page Mitchell's "The Crystal Man" from 1881.) And there had been previous movies and shows about invisibility, such as 1957's
The Invisible Boy, co-starring Robby the Robot. The '50s TV series
Rocky Jones, Space Ranger had a "cold light" device that rendered things invisible, and there were several 1940s movie serials that featured invisibility belts, rays, potions, and so forth, including the 1949
Batman and Robin serial. After all, invisibility is an easy special effect to achieve, so it was always a staple of sci-fi film and TV. Audiences at home would've been well aware of it by 1966.
