We do not write the way we speak. No matter how much I wish differently, people do not speak using what is often referred to as proper grammar. Not even this blog is written with completely perfect grammar because I blog according to my rules of speech, not my rules of writing. If we don't expect people to speak with proper grammar, then we shouldn't expect our characters to, either. Think about it. As writers, our goal with our characters is to create fictional beings that are as close to living breathing human beings (or otherwise, depending on your genre) as possible. That means giving them authentic dialogue, even if authentic in its turn means grammatically incorrect. The dialogue in your stories reveals scads about your characters, as you well know. Let's look at an example of what proper grammar and vocabulary can do for a character.
In the first Pirates of the Caribbean movie, Curse of the Black Pearl, why is it funny when Captain Barbosa tells Elizabeth Swan that he is "disinclined to acquiesce to [her] request?" (It was funny to me, at least, but I love dry, verbal humor more than anything else. Slapstick doesn't do it for me.) It's funny -- and unexpected -- because we know that those words should not be part of normal pirate vernacular. This formal language throws us out of the traditional pirate character paradigm, and not only do we chuckle but we also have to reassess our first impression of this character. We reclassify Barbosa as an intelligent man, not at all like the pirate buffoon scrabbling around on the floor for his wooden eye who couldn't tell an adjective from a barnacle. Now, that buffoon wouldn't be nearly as convincing as a buffoon if he were given grammatically perfect lines. In the same way, we as writers must check our dialogue and make sure it is appropriate to each character.
I'll give you an example from my own writing. I want one of the prominent character's in my novel to have dialogue that reflects his educated background. Therefore, I make sure that when he speaks, his grammar is as perfect as possible. But my main character is an entirely different egg. She does not share this sophisticated background. The novel is told entirely from her point of view. When I write her dialogue, and when I write her direct thoughts, I have to remind myself that the grammar rules of writing don't necessarily apply anymore. My goal is not to write as I have been taught by every university level grammar book I've had to study. My goal needs to be to write as I would speak. Let me rephrase that. My goal should be to write as any normal person would speak. That means she needs to finish sentences with prepositions, split infinitives, and commit other grammar sins every now and again.
I'm not talking about writing dialogue that's so full of grammar mistakes that the reader can't understand what the characters are saying. Read over your dialogue. Does it seem okay to you? Now, read it out loud? Does it sound a little stiff and formal? Is it like reading a school essay aloud? It's because we've been trained always to write properly. Take the sentence I just wrote. It would be perfectly acceptable in an academic paper, where the rules of grammar must be strictly enforced. But here's how we -- and our characters -- would say it: It's because we've been trained to always write properly. Splitting the infinitive breaks the grammar rules, but it creates an authentic character. Give your characters freedom to break the rules. Your readers won't care whether or not dangling modifiers make it into your dialogue (for the most part). They will notice quick as spit how natural your dialogue is, though.
Check out a grammar book from the library. No, I'm not contradicting myself, just keep reading and let me finish. Breeze through it, just review. You have to know the rules to recognize when they're broken. Once you've had a grammar refresher, start listening to the people around you. Pay attention to how they say what they say. (Huh?) Do they split infinitives? Do they use "a" before a word that begins with a vowel sound? ("a invitation" Don't get me started. It's painful just to write it) Listen for different ways that speech ignores written grammar rules. Make notes of things you like -- and don't like sometimes -- and start incorporating them into your dialogue. This is actually a fun exercise to get you focused on individual verbal idiosyncrasies and thinking about different ways to naturalize your writing. Written grammar rules do not apply to speech. Your writing should be polished and edited, yes. But your dialogue should be natural, with a smooth flow, and that means splitting an infinitive every now and then. To boldly go.