I am a Tennessee resident and also IANAL. I was about to get all up-in-arms and send an angry email off to Gov. Haslam's office when I read this story but, fortunately, I decided to actually read up on what this "new" law is. It is, indeed, an update to the Harassment laws on the books for TN. This law covers directed communication with a malicious intent. Simply re-posting goatse images on your blog does not put you in violation of this law. Re-posting goatse images with an attached threat to a specific individual or group probably would, though.
Should harassment be protected free speech?