It is ok to make mistake, that’s why we’ve been stressing that bloggers are not robots or computers, but human. But what readers can’t tolerate is a blogger whom when called out for a mistake would decide to either ignore or cover up.
When you are wrong, you are wrong. Owning the platform does not give you the right to be infallible. Have you not seen big brands like Coca-Cola and Toyota apologizing to customers for simple mistakes? Who are you not to accept that you are wrong?
You can post a false story and when that story is proven to be false, don’t stick to correcting the title by adding rumor or editing, simply attach and apology and reference the error.
Sometimes you can make a grammatical error and a reader might correct you in comments, acknowledge the correction and edit. Please be careful not to be confused into writing rubbish all in the name of correction. Use your sense to know what is right and wrong while taking corrections.
When you make a joke about sensitive event, apologize. When you are found in the most unlikely places, supporting the wrong causes or found disobeying civil laws, and the story makes it out to the public, apologize because certain people look up to you on your blog.