I've lived in Japan two years and echoing what the other commenter said, there's definitely crime in Japan, moreso in Tokyo, but it's usually more low key and I don't think as widespread (or violent).
- A delinquent student I had who dropped out in junior high caught up with me and told me how he went to jail and was a low level gangster.
- I also knew an Australian older guy who got jumped by some teenagers when he was drunk.
- Also a drunk guy tried to hit on a girl I knew while we were walking to the train station and literally tried to physically drag her somewhere and hit my other friend who wanted to talk to him peacefully.
- A creepy old guy showed two junior high girls a binder full of pictures of underage girls in a supermarket food court and was trying to proposition them or something. My friend used to be their English teacher and confronted him in Japanese. When I turned to look at the supermarket, everyone was dead silent mouth agape. The old security guard lady who worked there was crying.
- I believe I also spoke to a cop or an older person who said during the earthquake their was concern of people stealing or commiting crimes and they'd do it quietly.
- There's also the women's only train in place because of chikan or train perverts who try to grope women during rush hour. I don't know of many other countries that have it.
I definitely think Japan is one of the safest countries in the world. I left my phone on a bike and found it still there hours later, but there's definitely crime. I also don't know if it's great to conflate yelling, littering, etc. with crime, but there's definitely a correlation.