It's tempting to use stereotypes when you're creating a character because it allows you to bank on your reader's imaginations, their personal experiences, and yes their discriminations.
The fact is that not everyone from New Jersey sounds like the people on Jersey Shore and not everyone from the south sounds like they could be on a episode of HeeHaw. While it is important to give your characters flavor -- it is inappropriate to delve so deeply into a stereotype that the character itself becomes a slur.
There are other issues, of course, if you've ever read the Harry Potter books and you're anything like me there came a point when you started to absolutely dread any scenes that had Hagrid in them. It's not that I didn't get what he was saying. I understood all of his dialogue but it didn't make for a pleasant reading experience. I did eventually come to wonder if JK Rowling came to feel the same way about her choice when it came to Hagrid as he appeared less often in the series as Harry grew up.
And that's another issue -- if you make the choice to give your character a voice steeped in misspellings and abbreviated words in order to portray their accent -- you have to maintain it the length of the work. Characters like Hagrid and the house elves in the Harry Potter series are just an example of how much effort this could eventually come to involve.
Of course, there are sometimes when giving your character a little language quirk can only work to your advantage -- I doubt George Lucas ever regretted the iconic way he chose for Yoda to communicate.
There are ways to portray an accent without resorting to misspellings and shortened words. Listen to how people talk, not just the content of what they are saying. Seek out programs on television with people from different regions. If you want to hear southern people talk -- turn on CMT as long as you can stand it and check them out.
If you don't get it, don't do it. It's better to not take the risk with an accent and use standard English than risk doing it so poorly that you offend your readers.
A dialect is about diction, style, rhythm and pacing. A person from New York is likely to speak five times faster than a person from Georgia. An individual from Great Britain is going to use words that are not common in the US - you can pick up their slang by watching BBC America or you can portray their language quirks by slipping a single word here and there in.
The best piece of advice is to just LISTEN to others speak -- everyone (including you) has an accent. Record yourself speaking for several minutes. Read out loud to your computer if necessary -- try to speak as naturally as possible while you're doing this.