How to interpret NYTimes rental listings?

yes, you are correct. brokers list "made up" or old listings on nytimes so that you will call them, at which point they will say that the listing is no longer available, but they have similar apartments that they would be willing to show you...very likely at higher prices. same thing goes with craigslist and even the brokerage websites. It's ridiculous and it is one of the many reasons why I hate brokers.

Some listings with no address are not fake, but rather "open" listings. In NYC, many landlords use multiple brokers for the same listing. The broker won't list the address because they don't want to share their contacts with other brokers - not because they don't want tenants to know the address. When a client calls about that listing, the broker has to call the landlord/management co to check to see if another agency has already rented the place. If so, they have to break the news to you - sorry, no longer available - and try to find something else that meets your criteria. It's an infuriating system for everyone, though not necessarily a corrupt one.

But yeah: some of the listings are fake.

Tina
(Brooklyn broker)

I gave up using the NYT except in emergencies, i.e., tenants not renting from
my CL or SE ads, because in years past the Times allowed thousands of old and
rented apartments to stay on its site, thereby (i) needlessly cluttering the
site, and (ii) distorting current market values.And even then I only look at ads.

I stopped advertising there in the last century, although that sounds more
dramatic than it really it.

If you notice the same exact apt multiple times, it is likely a real open listing. I also like to check on what else the broker has listed. If you find a broker with 43 listings that have on/off histories that trace back months, run.

Am I correct to assume that NYTimes listings with addresses are probably legit?

If a NYTimes ad has an address, it is probably legit.
Streeteasy does not allow open listings - their policy is exclusives or co-exclusives only. The only downside of that is renters can't find legitimate open listings via SE, so it limits the pool. Especially here in Brooklyn, where so many of the landlords and management companies use multiple brokers.
People have been trying to fix this broken system for years, to no avail. It's one of the reasons I am a chronic buyer, rather than a tenant.

do not trust ny times real estate listings, even if it has an address!!! i was just scammed for thousands of dollars by what i thought was a legit advertisement with an address and everything about the building. the ny times does nothing to protect the consumer against this type of fraud. at least craigslist adds a disclaimer advising you of what to look out for with fraudulent listings. i am now left to resolve this on my own through the police, the district attorney, the fbi, and whatever other consumer protection agency there is. ny times real estate section blows!!!