I can't imagine an automotive engineer describing a new car engine as non-trivial or a painter describing his work as non-trivial.
Anyways, what words wind you guys up?
Edit: Happy Monday, btw.
Perhaps it is abused as a term by the population at large, but I'm reasonably sure it has its roots in theoretical computer science and maths. It has a meaning that is distinct from "complex". It means that something requires something more than pure mechanical verification or straightforward inspection.
A painter could use "non-trivial" in a sensible way. How much effort is involved in X? Well, it's non-trivial, because it involves more than having a look. It isn't estimating the effort, it is instead a binary classification - trivial and non-trivial.
Finally, to answer your question, I don't dislike individual words. I only dislike them once they are combined into sentences.
Everywhere else it's just pretending you do something important.
leverage
Paradigm shift - someone should invent a time machine and go back to shoot Kuhn's mother before he was born.
But non-trivial does have a specific meaning: it means that we don't have any code already written or proven technique that we can simply reuse for or apply to this problem, and some new knowledge will have to be synthesized, and there's a risk in making any estimates of time/cost until more is known.
edit: Oh and let's not forget Scott Adam's favorite: Synergy
It's one of the best tech words out there, it is very specific and there is no other good way of saying it without using a whole pile of words.
I also tend to hate it because I can tell before even starting to fix the kludge, it's likely to involve an large overhaul instead of a small bug fix.
(My brain always translates to turkey inducing...)
(Go watch 'In good company')
It seems that trepanation might be a good response to someone using this word.
"Could you drill down into my data set and shift some paradigms?" "Yes, and while I'm at it, I'll equalize your humours." WHIRR "Indeed."