Yeah but you think that they would have been more prepared as to the likely questions they would be asked by a listening station instead of waiting for them to be asked and trying to find the answers in a panic.
Even if they couldn't use the universal translator to respond because it'd be recognized, you'd think they could use it off the comm system. So when they ask a question, Chekov could repeat it to the translator, get the answer and Uhura could repeat it to the Klingons.
Does the translator work that way? That's a good question but if you don't understand the language, just repeating what the translator says could be just as obvious.
The novelization was interesting in that the listening post was bored, and either drunk or hung over. That, and it isn't the most honorable of posts
I know I have nostalgia goggles when it comes to TUC but it is still one of my favorite films. It has probably one of the most interesting introspections on the part of both Spock and Kirk. I think it also reflects the wear and tear that a war, even a cold war, can take on others. The psychological impact of viewing Klingons as enemies for so long, and suddenly they are attempting to make peace, it begs the question of how our heroes would respond.
Are there plots holes? Yes, but not ones that I find so grievous that I can't rationalize away or fill in the gaps based upon personal knowledge or the novel.