In the United States, at least, you can get any nonprofit's 990 form, either on their website or at www.guidestar.org. The 990 lists how much the top executives make, who their top vendors are, and how their budget gets spent.
Depending on the organization's lifecycle and purpose, about 15-20 percent of the budget on overhead is normal. A very new nonprofit has to spend a lot more on outreach and fundraising, as would a nonprofit that's raising funds for a major capital project.
I've found one of the most telling signs is a big gap between the CEO's salary and that of the next highest-paid staff. Unless there's some obvious reason (the CEO is the only full-time employee), that's the sign of a big CEO ego and a weak board.
The CEO and upper exec salaries should reflect their real market value, including the perks of the nonprofit sector. Most CEO turnover in the nonprofit world is voluntary, for example. In addition, the CEO of an organization with a lot of independent chapters has a lot less to do with their revenue stream than the CEO of one that's highly controlled from the parent organization.
Unless the organization is doing fundraising for a capital campaign, there shouldn't be big payments to professional fundraisers, compared to total income. Big consultant fees are another warning sign.