New York restaurants
An important note - do NOT assume that just because someone learned in a "top yeshiva" that his hashgocha is reliable.
There are multiple hashgochas out there where the rov relies on "daas yochid" leniencies that basically nobody holds of. Some rabbis are unfortunately ignorant of various halachos & scenarios - don't forget that there is no governing body that makes sure they're up to snuff. There are even certain rabbis who will not allow something into their own house when it has their seal of "approval" on it. There are also some clowns out there who simply do not have the presence of mind to be on top of what's going in the restaurant, like even bothering to check if the place opens on shabbos or if they maintain the slightest modicum of a kosher kitchen.
"Yeshivishe musmachim" from Tora Vodaas, Mir, Lakewood etc (some of whom I know personally), can be capable of anything.
The best thing is to ask people in the field if the hashgocha in question is at least up to the standards of a major national agency like the OU. (If someone they don't know calls them out of the blue & asks if a particular rabbi is "no good" they will probably beat around the bush in fear of a defamation lawsuit.)
Two independent organizations who monitor other hashgochas are Kashrus Magazine & the more "yeshivish" KIC, run by the Mirrer rosh kollel Rabbi Lazer Ginzburg & RAbbi Weiner. (KIC does not check up on any establishment unless they are more machmir, like keeping cholov yisroel & hiring waitresses who dress modestly)
While I agree with you that one cannot blindly rely on any hashgocha, I have also found that politics plays a large role in who is and is not deemed "reliable." This is not limited to NY either, but only seems worse here because the many competing hashgachos. I know of a case in another city where a restaraunt could not get the local vaad hakashrus to certify them because of a supplier that they wanted to use. This wasn't because that supplier didn't meet the vaad's kashrus standards, but because the vaad would only allow a purveyor who was one of that vaad's own clients.
And don't get me started on my issues with the KIC. While there is no doubt that many of the people who run and work in that organization mean well and do the right thing, I have noticed that some of their own "yeshivishe musmachim" can also be capable of anything.
With the KIC, restaraunt owners are in a difficult position. They are already paying a significant amount for a hechsher that their customers will rely on, and now they have this group knocking on their door. If they let them in, they now have to follow the directives of what is effectively a second hashgocha, or risk being blacklisted for something their (often better educated and professional) mashgiach told them was OK, but the KIC inspector, who can be following a "daas yochid" stringency, doesn't like. If they don't let them in, they're blacklisted by the KIC as "obviously having something to hide."
And who selects which establishments the KIC checks on? I don't know what their current practice is, but in the past it was complaint driven. What that led to was some hashgachos going to the KIC with spurious complaints about their competition.
IMHO, the whole operation stank from day one, and I don't know a soul who regards them as any more reliable than the hashgachos the KIC monitors. It would have been better for the KIC's rabbanim to have established a hashgocha that met their standards.