When I want to evaluate a charity I immediately go to guidestar.org and pull their most recent tax return.
I first look at the P&L and the balance sheet. The expense side of the P&L will provide clues to how donations are being spent. Also, I know of one nonprofit that has several years' revenue in reserves/investments. This is an organization run for the benefit of its management, who have years worth of job security and salary cushion if membership falls off.
In addition to salaries, I look at names. I remember one I looked where the old man, his wife, and his kids were all on the payroll.
I also look to see if the charity has for-profit subsidiaries. This is a completely legal shell game where, for example, they buy services from the sub. The sub is totally opaque, so it's a good place for nepotism, big salaries, etc. to be hidden.
I look at large outside contracts, too. Often there are printers, mailing services, etc. but sometimes there are fund-raising companies, etc.
Finally I look at the notes at the end of the return. This is where they are forced to explain things in the main return that are unusual.
All of that is just a smell test, because a good accountant can bury things pretty deep, but it's IMO still a useful exercise.