My current story is told in first person, and early on you realize he is not very bright. Is it wrong to use poor instances of grammar in his narrative to give him character? Example in question: “Hello, ma’am,” I stood the broom into the floor and looked at her and started blushing. I am just wondering if this sort of prose is acceptable.
It is, given the right story. In Flowers for Algernon, for example, Charlie uses incorrect spelling and grammar as he writes down his own story. The Sound and the Fury has sort of a different approach--no incorrect spelling but simple thoughts--which I personally like better. By the way, in your example, you can't separate the quote and action with a comma. You need a period.
I think if you are consistent with your "bad" grammar, then the tone will establish itself. It's something that can certainly be done, if you're doing it intentionally. Writers take all sorts of liberty with language in order to convey things about the POV character in first person. Try Riddley Walker if you want to make your head spin! If the main character isn't actively writing the story down, however, it might be an idea to avoid wrong spelling and wrong punctuation. If your intellectually challenged character is telling the story, or just thinking the story—rather than writing it— spelling and punctuation won't be an issue. So, for the sake of your readers, maybe just stick to the bad grammar constructions? Again, not a rule, just a suggestion. As @lustrousonion pointed out, do watch the comma splices.
Oh, fair enough. Those pesky edits! I've discovered many a grammatical error in my own MS caused by changing one bit and forgetting to change another so the grammar agrees. Aargh...
I think it's a great way of adding character. I don't see any problems with your example. At the same time, I'd try not to go overboard with it to the point that it could be confusing to read. I read a book once (in first person) where the author wrote 'summat' instead of 'something' in the first line. Most readers in England would recognise the pronunciation, and it gives quite a lot of information about the character (class, area) without going into explanations. But he didn't do it with many words, and he kept the grammar simple but clear. I think you can pick and choose how you approach that kind of technique, but don't try to do it with 'everything' - spelling, grammar etc. Just a couple of anomalies can have a huge effect.
Yes, I think you should write it the way that your character would talk. Otherwise, it's not really his authentic voice, which is part of the appeal of first person. That said, misspellings etc. are confusing. Don't go over the top to the point where the reader must reread the sentence several times before they get it. Just a warning you probably won't need: make sure you don't give the impression of making fun of the character, or worse, uneducated people in general. Just be moderate in your use and I think you'll do fine.
I think it can be a really effective tool when handled well. There's nothing I like more in a first-person story, than to read a narrative which possesses so much style I can literally hear them telling the story and see their arms waving about.
I'm trying out something similar for a story I'm working on. Very difficult to keep it up and keep it coherent. I prefer deliberate grammar flukes to misspelled words. Not sure why. But I've read a few vintage stories where a side character had the stereotypical black southern accents ( and the writer used creative spelling ) and whoa nelly they were hard to get through.
You want to give Irvine Welsh's Trainspotting a try. Even as a Brit where the Glaswegian accent might not sound quite as foreign as it does to others, I find it nigh on impossible to read. As an example, this is the first paragraph, as it appears in the book:
I can't read a book after watching the movie because I also know pretty much what's gonna happen. But I get the point.