How big a role does the consideration of these things play in writing stories, whether short stories or longer pieces, i.e. novel(la)s? I feel like it plays a much larger role even in mediocre books, than I perhaps ever give credit for. I also feel like that's a big reason for why my writing tends to fall off a cliff in short order, before the entire spectrum of a particular idea really takes off. It's as if I've run into a wall with the way some of the things I write are worded. Any thoughts?
By mechanics, I assume that you mean grammar in general. If you mean subject/predicate agreement only, then I'd say that it is very important in writing. In general grammar is very important in writing. I feel as though a comprehension of what is right and proper is not only important, it is necessay for a writer. Then after you know all the proper rules of grammar, if you choose to break them, it is with purpose or for effect.
I'm more referring to the decisions one makes between two or more options, particularly when all options are correct.
Bad grammar will disturb the reader and may make reading a pain, even if the plot, characters and descriptions are excellent.
I would say variation in sentence structures should be taken into consideration. Like for example in first person narrations, there tends to be lot of 'Is' followed by the verbs.. I sat, I stand, I saw.. I went to his house. I saw him leaving. Can be written as: I went to his house. He was leaving. This is true for third person narrations also. Another thing we may consider is the sentence length. Variation is always good. So, we have to decide the structure according to the length of sentence we want.
Variation in your sentence structure is something you should not only practice but should also have a firm grasp of why one structure would be chosen over another. Let's use Manav's example and expand it a bit: I went to his house. I saw him leaving. He got in his car and took off. I got out my keys and went to my own car. Do you see how after a few sentences this starts to sound like dinki-dinki-dinki-doo, dinki-dinki-dinki-doo, dinki-dinki-dinki-doo....? The lack of variation sets up an unintentional rhythm to the read that is annoying, flat, and without any subtlety.