Anybody know anything about this building? I heard it a rumor that the the building owes the city a lot of money and the city may take it over. I heard another rumor that they had been some sort of govt. backed cooperative (not Mitchell Lama) and are trying to get permission to privatize.

See:
http://a836-acris.nyc.gov/Scripts/DocSearch.dll/ViewImage?Doc_ID=2012122400052001
which is a recent document amending previous "indentures" under which the building owner (Turin Housing Development Fund Company Inc.) does appear to owe NYC a significant sum dating back to the 1970s.

The previous documents should also be available in ACRIS, and you can see all the other financing/transactions.

So how does this "indenture" affect the buyer? I see someone is asking for an all cash deal of 399K on one of the apartments. Does the "identure" mean it's hard to find a bank that will give a mortgage, so they're asking for cash?

Did you ask the seller/broker what they know? They should at least be able to discuss the reasons cash is requested.

It does sound like there's a complication of some sort, but it could be any of a number of aspects -- who owes the money (coop vs sponsor), the governmental nature of the loan, or the magnitude of the loan in relation to the building's income or asset value.

I don't think this forum is going to provide the detailed answers you would need in order to proceed. Seek advice from an attorney who has experience in coops with HPD involvement.