I really think the title should be ‘Safety in Japan’ than the former because in the 2.5 years here I have never felt threatened or unsafe here. Infact if you loose your stuff in the train, you are most likely to find it back if you to the ticket counter and say 忘れ物(Wasuremono). They have some English assistance and can help you find your bag. Generally, the lost property is stored in the last station of the the line you took. They will ask you general details about the time you got off the train, the size, color and the stuff inside the bag etc. so be prepared to answer these. Once, they are sure its yours they will give it to you. Around 5 of my friends have forgotten their I-phone 6s in the train and got back in 2 weeks, and in some cases very quick like 2 days!!
There is theft hard to be seen in Japan except the red light districts of Roppongi and Shinjuku if talking about Tokyo since they are full of muscular bossy sales people selling all sorts of stuff which are illegal elsewhere. Mostly they are foreigners or 外国人(gaikokujin) who are involved in these activities, but please be careful in these areas especially at night.
If you go to lesser known cities or even the 2nd biggest city of Osaka, things change and you need to be a little more careful than Tokyo but overall Japan is very safe for travelling.