Some will have snags with permitting, some will have contractors you need to fire and then pay more for a new crew to come in and fix the job.  

What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

Very subjective question based on your investment knowledge, home market, investment strategy and requirements. 

The high end is the 20 or so co ops on 5th Avenue or Park Ave (one is on East End Avenue) that require liquid assets of $100 million + to gain board approval.  

For example the license should not only have a cost but also require at least some compliance training targeting some of the most common issues/complaints.

Definitely will bring more jobs and with that the workers' families.

No offense, but hire a PMC because:1) You hate the process of placing tenants.2) You didn't do a very good job of screening the current ones.Sometimes we have to get out of our own way to find success!

I'm fairly new in the industry as well, and most of the sources I've checked at first require a subscription (CoStar, WSJ), but I found this newsletter called Zeroflux Real Estate who consolidate real estate news from such sites.

The standard rule is $250k per person who legally owns/occupies for the 2/5 year requirement. 

Unfortunately NY requires a RE license to wholesale in the state.