How often/long can you go to Japan as tourist? I was in Japan 16 days earlier in October. I'm from Norway so don't need visa. So my passport has a sticker in it which says 3 months "landing permission" or whatever (until Jan 7th). I would assume I can return to Japan whenever before that? But then what about after that?
That temporary Visa is valid for that particular visit. You get a new one when you travel there again. http://www.no.emb-japan.go.jp/Norwegian/Reiseinformasjon/visa.html#Temporary
You can have the standard 3 months then you could try to get an extention but the imagration don't have to award this to you. Anyway, the longest possible stay would be 6 months.
I used to remain three months, take a few days in Korea, then come back three months, then... Does it still work?
So to get a specific answer; if I was there 16 days in October on a three months permit, will I have any trouble going back for another 16 days in December?
It depends on the immigration official. Generally (back in the day) the first one wasn't so hard. With each addition attempt it became more and more difficult. Not sure how it's working now.
you should be okay - they're looking for people going in and out of Japan at the end of their 90 day period, going to Korea for the day, then flying back in. Basically : suspicious patterns that looks like it maybe deliberate abuse of the visa system.
Your from a visa waiver country which allows you up to 180 days stay a year. Two short trip will not be any problem, immigration are only really looking for people who look like there trying to stay the maximum duration. I've had three trips in a year before with no issues, as long as you have a return ticket and funds they won't question you.