Put yourself in your reader's mind. You’re reading an email from a business professional or a great blogger you admire and come across a spelling mistake. And another. Then the incorrect use of an apostrophe. And another spelling mistake.
This stunts your flow of reading as you stop at every error because the sentence doesn't make sense. As a reader, this effects your view of the author, either consciously or subconsciously. At worst, you'll think less of the author and stop taking them as seriously. Now, I'm not talking about one mistake in every four emails. We're all human. No one is going to think less of you for something that rarely happens. However, what if someone new read that piece of content as their first impression of you. They may not come back.
Remember, you are writing the email or post on a computer and there is spellchecker and other software like Grammarly to check your work. Use them. Another way for you to spot errors, ones that the computer may not flag, but that stop the flow of the piece, can be seen after leaving your work to rest for a day or so. Your short term memory forgets it and therefore you see your work almost as an impartial person. This does mean you’ll have to create your content early, but that is the best practice anyway in case something comes up.
Consistent incorrect spelling and grammar could also effect your SEO rating, since the correct word won’t be seen. The search engine can only pull what you put on the site. Even someone searching who types incorrectly in the same way will receive a did you mean message from the search engine to put them on the right track, so make sure they will find you.
Attention to detail is important is more than just grammar. If a piece of site artwork doesn't relate to the rest of the content on the page, you do tend to look like you didn't take the time to check your work. And often the reason you don't take the time is because you don't care. And if your spelling and grammar aren’t checked, the reader, or your client, could expect less attention to detail across your work. So take care. Check your work. Get someone else to check it.
Put the effort in and your hard work will be subconsciously noted by your readers.