Have not seen it often but it does happen
In my 32 year airline career I have seen just one such detailed check as described by cactusbusdrvr. It was Christmas day a couple of years ago in NRT arriving from a US gateway city. When the jetway docked with the aircraft 4 Japanese Aviation Inspectors boarded the aircraft. Two of them proceeded to the cockpit identified themselves with credentials and informed me as the Captain of the aircraft/crew inspection. The remaining two inspectors were there to conduct a cabin inspection and introduced themselves to the lead flight attendant. Each team of 2 inspectors had a lengthy checklist that included all the items mentioned by cactusbusdrvr. Every conceivable item you could imagine related to the operation of the flight and aircraft was on the two separate checklists. The inspectors checked extra sets of glasses, confirmed flashlights worked, examined ops certificate and insurance paperwork. The inspectors who I would say spoke level 4 English had separate checklists for the cabin and the cockpit. They did examine our inflight paperwork which we had to retrieve from the cockpit trash bag and were surprised no archiving was required for that flight. There was a rather extensive discussion of our arrival fuel which was well above the required minimum. They did not retain any of the flight paperwork, I am not sure if this was because of the coffee dripping from the flight plan after retrieving it from the trash bag. No questions about operation of the aircraft or aircraft systems were asked. The cabin inspection was also very extensive, checks of all lighted signs, fire extinguishers and every item of emergency equipment were examined. Flight attendant manuals were also checked as I recall. The inspectors were exceedingly polite during a very extensive 45 minute inspection. As chance would have it in my recent training for this aircraft I had received a 30 minute class on how to accomplish an aviation authority inspection in a foreign country. Never a topic for a training class I have seen before or again but exceedingly valuable as we had recently switched to all electronic certificates of insurance and ops certificates. This seemed to be the first time the inspectors had seen electronic documentation and there was several minutes of discussion amongst themselves in Japanese over these items on their checklist. I will not say it does not happen but in my 30,000+ hours it was only the second time I have received an inspection from an aviation authority other than the US FAA. The first was in Managua years ago on a divert there for a maintenance issue and the inspection was very brief and administrative, licenses and medical certificates.
As cactusbusdrvr observed from the email posted there is always a chance of an inspection anywhere in the world. With the recent switch to all electronic everything that seems to be taking place one might want to take the time to locate the appropriate documents for operation of the flight and aircraft. The class I had received on aviation authority inspections in a foreign country was invaluable on this topic.