"where image takes precedence over wisdom where sound bite politics are served to the fastfood culture where straight teeth in your mouth are more important than the words that come out of it"- From "Television, the Drug of the Nation" by The Disposibile Heroes of Hiphoprisy
Is it important to speak and write with correct grammar and spelling? It is, but not for great reasons.
Like manners, grammar and spelling are social conventions. There's nothing inherently good or bad about the way things are said. Societies agree on how to do things, and we get irritated if those rules are broken. As a result, your message will be more poorly received if it's got grammar or spelling errors.
Ideally we should try to understand the content of what is being communicated, and evaluate the communication on those grounds. Fight the temptation to disregard the content of what is being said based on grammatical and spelling errors. If you bristle at this advice, ask yourself if you think it's okay to judge what someone's saying on their physical attractiveness, teeth straightness, or how good their breath smells.
We're more likely to listen to and believe an attractive person, but that's not a good thing. One of the most irritating things in the world is a person who finds grammatical errors. More specifically, the people who can't keep it to themselves are irritating. Some of my readers might be bristling at this too, thinking that people should use correct grammar.
The problem is acute with our evaluation of foreigners. Our perceptions of people's intelligence is greatly affected by their fluency with language. This explains why we tend to think non-native speakers of our language are stupid. I hope all of my readers can agree that you shouldn't be too nitpicky with grammar when a foreign speaker is trying to tell you something important.
Grammar and spelling are only important because people think it is. As you listen to people, try to be better. Strive to treat it like physical attractiveness-- it's the gift that matters, how how well the bow is tied on the box.
Pictured is an octopus.