Testing of isotope ratios in tissues may point to the country of origin of the homme de la rue. Such results may be able to point to a particular region of the home country.
To turn it around a bit, here’s a scenario that must occur pretty frequently:
A body is found in the Arizona desert, near the border. There is no ID. The man appears to be hispanic. His fingerprints do not appear in either the US or Mexican databases (or perhaps the body is too badly decomposed to get fingerprints).
What happens now? Does he end up in an unmarked grave, or do the authorities go to further lengths to try to identify him?
Such bodies are often dehydrated by the elements, leading to a mummified corpse. There is a process by which such bodies can be rehydrated sufficiently to take fingerprints.
If the fingerprints don’t identify the body then strontium isotope ratio testing may narrow down where the person was from.
If isotope testing fails, then a burial in a potter’s field is likely.
Identify an American abroad? That’s easy-- he’s the guy with the fanny pack! 
Need answer fast.
Damn. Whatever it is you’re eating, you need to cut back. Dead unidentified foreigners coming out of any body orifice is just WRONG, no matter what country you’re in. 
There may be clues to Americaness on a body without ID. Like say a beer gut or a Yosemite Sam tattoo.
Would a regular detective and coroner put in the work to identify serial numbers from surgical devices and the quality type and age of dental work for a Jon Doe, or is that just something from books?
Nah, Aussie would be my first guess.
It just goes with the territory when you eat too much spicy Thai food.
If the world is like it was in the 1950’s dental techniques are different around the world so maybe that’s true, and your dental work could make someone say "oh, those are american fillings.
Surgical stuff (like the titanium screws in my head) are also unique to some countries. I understand that larger surgical implants (Like artificial knees and hips, have numbers on them to identify the patient).
An American detective/coroner would do that work, yes, and I’d expect the same to be true in Canada, Western Europe, Australia/NZ, and similar locales. In less-developed countries, I suspect there is more variation, and probably more than a few that would expend little or no effort.
That’s putting it mildly. Thai cops will trample all over your typical crime scene, dropping cigarette butts, spitting, all the while wishing they could just get out of there so they can go visit their mistress.