The problem with the idiot training his dog to do a Nazi slaute was that he accompanied it with the words "Gas the Jews". While I dont beleive the guy was a raving anti-Semite who revelled in the Holocaust, what he said was an incitement to hate, and as such he deserves to have legal proceedings taken up against him.
If nothing else it will teach him and others to think before posting such stupid sentiments to social media. Its fine to say "gas the Jews" and giggle amongst your meathead friends, it becomes something different once you publicize such views openly.