If you're writing a piece that's supposedly written by a person who's not very educated in first person POV, is it ok to use bad grammar on purpose to help convey that point?
Sure. Just be careful that you don't overdo it. A little bit can be effective at creating the impression, but too much of it can do more harm than good in terms of reader reception.
Read something by Jose Saramago. He definitely has an interesting way to write dialogue, which most people would call purposefully bad, although for him it's not the characters using bad grammar, but the author. It's okay to do it like that, but it will put off some people if you make it so bad that it's hard to understand it.
I have a couple of characters who speak very poorly. Very blue collar combined with lack of education. It is like pulling my own teeth to write like that. It is all "Huck Finn" and hillbilly and redneck. I don't notice at all, when I read it, but writing it is sooooo difficult. My Facebook friends and I will make Grammar Nazi posts to annoy one another. "Your gonna luv there comments Dave. This post is where its at!" "There, they're, their. It'll be okay." Sometimes I have to go have a lie down after reading them.
I have a couple of characters in my novel who are ungrammatical speakers, so I know what you're up against. I'd say in this instance, less is certainly more. Don't overdo it, especially if the characters have a lot to say—because too much bad grammar makes difficult reading. But definitely do it!
"Your gonna luv there comments Dave. This post is where its at!" "There, they're, their. It'll be okay." I know these were in jest. But to be clear, homonyms and mis-spellings do not belong in uneducated speaker's dialog because they do not change the sound of the words. They just make it harder to read. Phrasing, word substitution, shortening -ing to -in' , etc., in moderation can be effective.
are you only concerned with dialog, or are you referring to the narrative, too, if a character is telling the story in first person?
It is best to introduce the character's grammar, accent, patois at first appearance, then let it slide away. The reader will remember without having to be constantly reminded. It is like a limp. Show it to us, but don't constantly point it out throughout the work. If it-limp or grammar- serves a purpose, (" he had trouble with the stairs, and lagged behind the others") then it can be used. Judiciously. My MC is from eastern Europe, traveling in America. His very first words are: "Excuse, please. My engine is hot. Can you look?" Other than having trouble understanding conversations when he hears 'copious' or 'moribund', his speech thereafter does not bring Sasha Beren Cohen to mind.
As with all things, it's fine when done well. Flowers for Algernon slides the prose from one end of the spectrum to the other and back again, as the POV character goes through some profound mental changes.
I did this for a short story called Thunderbolt written from a con's pov. It's on my blog if you want to check it out. It got mixed reviews as the dialect could get on a reader's nerves. A few said to keep it dialogue only, others were absolutely fine with the narrative. Some thought it was great others couldn't get through it. I think it all depends on how well you handle it, plus your audience. No matter how it goes some will hate the device.
Sapphire's Push is written in very bad grammar on purpose, though it got better as the protag learned to spell better. I think it was marvellously done, and I just devoured that book like in two days. Sure, at times you have to stop and think, read the words aloud to decipher the meaning, but why not challenge the reader a bit? I say, go for it, then have it beta-read, and you'll get some idea how well you're pulling it off. In my and T.Trian's current WIP, the MC is Swedish. Guess if she speaks perfect English? Good thing she isn't very talkative...
the best-ever example of this technique are the classic short story and subsequent novel, 'flowers for algernon' by daniel keyes [movie version, 'charly']... it's written as a series of reports/observations by the main character, charlie gordon... as his low IQ soars to amazing heights and then drops back to his original 'retarded' level, the writing goes from misspellings and poor grammar, to lofty scientific rhetoric and back to barely literate... brilliantly done!
I totally forgot about good ol' Huck Finn. I have it on my shelf too! First person is a completely new thing for me, so I'm trying to find my way around here since my next two pieces are planned to be in 1st person, present.