How do grammar mistakes impact negatively on the reputation of a blog?

Grammar  mistakes weaken writing structures >> Weak structures reduce people passion towards your blog >> Less passion means high bounce rate >> High bounce rate means bad present in Google, bad SEO practice and your business is degrading. The problem is all make mistakes, so it is important to review contents again and again and to benefit from what called "Proofreading". 

Make grammatical errors and you will start losing your audience. And you don't want this.

They make the writer appear unprofessional and uneducated along with attracting the types of people who love to start conflicts for one simple mistake; ignoring the rest of the written piece. (Seen from personal experience) As far as reputation goes, it breaks down into the writer himself and the visitors common on the blog therefore, it can impact reputation by the people it attracts and those who comment as well.

Grammar mistakes are a tragedy to writing. It ruins your entire work. Let me cite some common mistakes.

1) If you intend to express your delight over a very well decorated and designed home, and your statement runs this way: "My friend's house is very homely. I love the way she decorated it." Then, you are just confusing your readers. 

- homely (notice the letter "l") means plain and unattractive.

You should have written your sentences this way:

"My friend's house is very homey. I love the way she decorated it."

- homey (that is without the letter "l") means cozy and pleasantly comfortable.

2) Be careful in using these words

     - there and their

     - its and it's

     - whose and who's

     - too and two

     - too much and so much

These words may sound the same, but their meanings are completely different. There are a lot more homonyms in the English language that you should take caution in using.