1. Do authors publishing pieces online care less about spelling and grammar?
No. A byline is a byline. Anything that appears under your name in a formal setting should be spell-checked, grammar-checked, and coherence-checked. I say “formal setting” to exclude media such as smartphones.
2. Do online audiences care less about errors?
Depends on the context. If you’re sending an e-mail or a tweet, typos are all-too-common. But if you’re writing a blog post or e-newsletter, then audiences expect a higher quality of writing, in which typos and sloppiness are a turn-off.
3. Do you personally care about such errors?
Absolutely. In fact, I recently stopped reading an e-book after the third page because it contained so many typos. If an author doesn’t care enough to check his own work, that evinces a lack of respect for his reader.