In keeping with the words that "do not...mean what you think it means", this is a classic. When you get the reference, you'll understand why.
Like many words starting with "in" for "not", their given etymologies make you hunt all over a dozen other words to find what is really means. Conceivable comes from Latin "con" for "with or together" and "capere" for "to take" as the latter was derived from the Indo-European "kap". The Latin derivative was "concipere" which then became "conceivre" in Old French. Add a little suffix, "able" meaning "capable of", e voilà, we have "incapable of being taken with or together". Inconceivable. Yep. That does it for me. Not. Back to conceivable. Conceive generally refers to pregnancy, with a secondary meaning of creating an idea, not just life. [Ed. note: conception is not a related word, but there is the similar pair of concept, as an idea, and conception, as an creation of life which is interesting.] So, by extension, inconceivable should mean incapable making life. But inconceivable has no element of "life" associated with its usage. Somehow, c. 1631 when this word originated, creating life wasn't as important as stating what couldn't be understood. So the implication of creating an idea from conceivable became not being able to understand the idea for inconceivable, which is an incorrect negation of conceivable, which should instead be unable to create the idea. And we are left with the usage of "unimaginable, unthinkable and unbelievable". Oh, well, it wouldn't be the first word which etymology to usage is slightly askew.
That said, the usages of inconceivable, notwithstanding the movie, are pretty straightforward. It is inconceivable to me that people would not use the subjunctive tense, while it may be inconceivable to many more that the subjunctive tense still exists. The jury found Plaintiff's counsel's theory of the case inconceivable and awarded a defense verdict. I'd probably just go with unbelievable, but inconceivable adds a meta level to the unbelievability. Not just that the theory was unbelievable, but you can't imagine how anyone else could believe it. It is completely incapable of being grasped by anyone. Quantum physics, black holes, and imaginary numbers should be inconceivable, and once were. The homecoming queen found it inconceivable that she would not be admired by the entire school. A bit banal, but it does the trick.