I think it's fair to say that if your threshold for being able to enjoy Star Trek is that there can't be an obvious plot hole, idiot plot point, or technobabble inconsistency in any of the hundreds of episodes filmed...you might as well walk away right now and not waste your time. Because it will disappoint you. Or just watch it and take a drink every time they 'reverse the polarity' of something to get out of a seemingly impossible situation. 🤣 It's a utopian escapist fantasy for me and I love it, flaws and all. I
want to enjoy it, and that's why it works for me.
To be fair, even
real-world theoretical physics doesn't have that level of ironclad internal consistency.
As an aside, the TNG Blu-Ray box set has some great interviews with the writers, which I thought provided a LOT of really good insight into how the show was written. One thing they mention that is very important to remember: for most of the show's run, they were writing furiously to meet deadlines, and in constant fear of cancelation. They didn't have time to ruminate at length on every plot point or writing decision. This is true of most TV shows, but some of the 'bad' writing was the result of tight deadlines, burnout, producer/studio interference, the writer's strike during season 2 and so on. Under the circumstances, the fact that
TNG still holds up is a testament to the quality of what they did, imperfect as it was. And IIRC,
Generations was written in parallel with part of Season 7, so the writing crew was stretched really thin at times.
The frequency had to be displayed, to make the stupid plot point work. Gordy wouldn't have been constantly looking at the display, given the work he had to do.
A better (writing) solution would have been to have Geordi walk past the shield generator during his daily rounds - his visor would register the shield frequency directly from the generator itself - he doesn't need displays to know what frequency something is! - and the Duras sisters could have gotten it that way without it needing to be (carelessly) displayed anywhere.