Do they check overseas records?
There are some things one can induce — especially from the fact that some institutions are required to inform you (depending on the country you're from) if someone — be it government or non-government — looks into your record (for example, a United States credit check).
It's reasonable to assume that the domestic (Japanese) checks would be quite thorough as officials would know what certifications are like and could easily communicate during work hours in a language using procedures and forms they're comfortable with.
With foreign countries, it's not so easy. Most foreign countries, with the exception of things like the INTERPOL database and the Schengen Information System (used by European countries) used during country entrances and exits, make it very hard for foreign entities to probe into matters of their own citizens in the name of sovereignty. Looking into things like educational background these days get referred to specialized database agencies which require one's consent to release the information unless it's simple matters such as years attended and whether they graduated or not.
The Ministry of Justice can also omit many of the procedures it would normally do for someone who is just immigrating to the country. A naturalization candidate would have already been living in Japan for many years and probably been checked by immigration many times, making it unnecessary to check the same things that immigration has already checked.
From my personal experience, in cases where they needed to verify something (for example, they asked for my transcripts in addition to my degrees), they ask you to obtain the certified records and provide it to them. I checked other systems in America that leave a "trail" (a record showing who has looked into my records) and there was no record of Japan or anybody else looking into them.
The Ministry of Justice has access to the same databases on foreigners that immigration has, which is primarily a cross-country INTERPOL database that gives them access to criminal histories and terrorism / national threat level scenarios. Japanese immigration supplements this data with their own domestic databases containing fingerprints, country entrances and exits, and domestic crime and immigration records.
If it is ever discovered that documentation used to obtain naturalization is falsified, your citizenship can in theory be revoked after it is issued on the grounds that because the conditions for naturalization were never met, one was never a Japanese citizen and thus the naturalization is annulled in a process called administrative denaturalization. However, if you have naturalized and already lost your original citizenships, Japan would probably not denaturalize you (which would make you stateless). They would most likely imprison and/or fine you, as providing false information on a government form is a crime.
