when you visit the Kodokan, you can only join the regular (instuctional) class if you're going to be there for awhile. if you're only visiting for a few days or 1-2 weeks, then you have to goto the randori free class (anytime between 5 - 8pm, every night except Sunday), which is what I did. So I can't speak from first hand experience on what they get taught in the Kodokan classes, though from what i saw several times, the people in the classes seemed to spend alot of time on breakfalls and gokyo -- NOT competition techniques.
in the free class (which is actually the mat on the near right) there's no one "teaching" and you just ask people to practice with you: uchikomi, newaza, randori, etc. FYI: the instruction class is either on the far left or right, depends on what else is going on.
in any case, most of the people you run across don't speak english, so unless you speak Japanese, most of what's learned by training there (as a visitor) is from observation and trying out what you see others do. however, in the spirit of judo, and if you're respectful, some people will stop and try to explain things to you. actually, some of the stuff i still use today are things that ironicially 2 Canadians who've lived in Japan for a long time showed me. one was a 6th dan and had been there 19 years; he showed me some stuff on taiotoshi. the other Canadian (who was from Hamilton) showed me stuff with uchimata.
anyways, the bulk of my technical training in Japan happened when I trained at the high school and university that i was at. specifically how to get certain grips, kuzushi, and throws that work better together in combination, how to fight people of ALL sizes and what to do vs. guys much bigger than me. But i think more than anything "technical", what i learned the most about was having a fighting spirit and the mentality of judoka in Japan. its nuts! :)
BTW: my first time to Japan was in 2001, when I was an orange belt, I called the Kodokan and asked if I could train in the randori free class, they said no. why? brown and black belts only. In 2002 I was a brown and that's when I went for my study exchange. However, getting to the Kodokan was close to an hour away, and being on a student budget again, it wasn't my priority to get to since I was already getting pounded on campus regularly. afterwards, from 2003-2005 I went back to Tokyo every 3 months on business and thats when i mostly trained at the Kodokan. I even left one of my gis chained up in the foreginers change room for most of 2004-2005, before bringing it back to Canada. and yes i washed my gi! My hotel was 5 mins from the kodokan and they were familair with laundering judogis (Tokyo Dome Hotel). I left my gi in Japan since I didn't want the hassle of packing one every 3 months.