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

I would give them suggested vendors, a consequence for failing to complete, a deadline to complete the work, and notice that I will inspect to verify the work is done to my satisfaction.After notifying the tenant, then I would contact the owner (phone or email, depending on their personal preference and my time) and let them know what happened and how I'm addressing it. 

Verifying last 2 years of rental history very important!

If you choose to proceed, I recommend verifying the source of the funds as it could be tied to a specific type of compensation.

Are there any free public sites to verify criminal and rental history in california?

They may need a notice to quit their services, which may include listing. better to follow up on documentation to verify. 

There's a variety of ways to get a deal in front of you (I'm mostly a flipper), but basically if it looks promising, I run custom comps queries and check the current & past $/sf of renovated/distressed product in that city or zipcode.Here's a chart on 90066 I generated from my tool under Market Stats > Sales Data > Specific Zip Code:- My above chart (more available) shows the Avg Renovated $/sf (High) over time in this Zip Code, something completely different than charts/providers based on Averages/Medians only, like every other platform (RedFin Below, https://www.redfin.com/news/data-center/):- Can't select smaller locations such as City or Zipcode for their $/sf data, so it's useless helping me underwrite/verify a deal.- Can set Zip Code for Median Sale Price data, but again it's the median/avg so it's useless helping me underwrite/verify a deal.Then if that looks decent, I'll run Sales Comps, and get a quick summary of some key metrics based on those comps.

They are very strict when it comes to verifying experience.

I only needed to verify them and generally their conclusions, but there was no sense in reinventing the wheel from scratch. 

To what extent should I be verifying that they have the correct licensing?