Health Insurance would not be a problem as National Health Insurance is available to all residents as Maciamo stated so that would be taken care of. However, the quality of health care by Japanese doctors has been questioned in the past.
Property insurance if you live in an apartment or rented house is also available.
Retirement homes, now that's another matter as they are a rarity in Japan due to the custom of the eldest child caring for the parents and the stigma attached to those that do put their parents in one especially if they are healthy. As Maciamo pointed out, there is a waiting list for the few that are there. However, I prefer to not think about that at the moment as long as my wife remains healthy.
It has been reported here in the states on "60 Minutes" and elsewhere in the news recently, that medical care in Thailand hospitals, while being 1,000% cheaper than here in the USA, is a very viable alternative and one that is gaining momentum.
The reason given is that nearly 100% of the surgeons and doctors have been trained and interned in either Europe or the USA and are qualified to work there if they so choose. Also, the facilities of the best hospitals that treat foreigners are 100% state-of-the-art. India is also a great alternative for major surgery.
Check out this article
Also
here is another article dated Aug 16, 2006 on a US company that is encouraging it's employees to have surgery overseas to save on costs.
Should I myself ever need major surgery, either while living in the USA or in Japan, I will definetly consider and probably use this alternative to save on costs as the surgeons are no less qualified than those here or in Europe.
As far as pensions and such I will not be able to collect from the Japanese as I never put anything in. However, we have prepared saved enough that that will not be a problem in the long run.