Japan isn't exactly like any other country. If it was why would you specifically want to come live here?
One thing to note is that Japan doesn't really have immigration as such. Certainly not like it is in say Australia, where I'm from, which has an annual immigration intake of well over 100,000 people. They just don't really do that here. They'll let you stay if you have a sponsored work visa or you get married to a Japanese national.
Generally these days you'll only be able to get a 1 year sponsored work visa that can easily be renewed each year through the same company or another one. After 3 years with the same company they'll normally grant you a 3 year visa. If you haven't married a Japanese national during that time you'll need to be here approximately 10 years before you can apply for permanent residency.
There are lots of foreign owned companies with branches in major cities throughout Japan and it is these companies that you'll have a decent chance of getting a job that is not english teaching related. Having fluent Japanese is often not essential at all at these companies. Conversational ability is often enough.
It's not incredibly hard to get jobs here but you're not just going to walk into jobs that a Japanese national could do just as easily. This is why most opportunities are either in the english teaching field or with foregn owned companies.