It all comes down to if you can speak it. If you can read the text aloud and it sounds natural, then go ahead and toss grammar out the window. Human beings often don't speak in complete sentences, and we can handle reading fragments as long as there's a purpose. As with any rule, you should have a purpose when you break it.
Say, dramatic timing.
But if you can't read the thing aloud without cutting you tongue on broken sentences (coughcormacmccarthycough), you may need to fix a few things. The best thing to do is to trust in the eternal wisdom of Duke Ellington: "If sounds good, it is good."
As for using apostrophes to signfy accents in dialogue, it can be a nessary evil. But like all nessary evils, its not one you want to use often. Look at how Anne Proulx and Elmore Leonard deal with backwoods accents, with as few apostrophes as nessary. In particular, I'm thinking of the dialogue of Raylan Givens, Leonard's protagonist in Riding the Rap, who sounds country, but not like he's trying to talk around a mouthfull of pebbles.
For more of a genre element, listen to how the dialogue is constructed in Firefly. Almost every character talks in a pseudo-country patois, but each in a different way. You could write out all of Mal's dialogue without a single apostrophe, I expect, and it'd still read like Nathan Fillian's says it. Jayne's lines would prob'ly have an apostrophe or two, though.