I use guidestar.org to get nonprofit tax returns. If you're not used to reading this stuff, you might want to get someone/a CPA to help until you get the hang of it. I look for things like:
High staff salaries and names that look like dad, wife, and kids. i.e. nepotism
High expenditures for fund-raising.
Other high expenses (travel, entertainment, etc.) that take away from money used for the charitable purpose.
High balances in reserves unless the organization needs handy cash to deal with emergencies like epidemics, natural disasters, etc.
Suspicious expenditures to outside organizations.
For-profit subsidiaries; this is a good place to hide bad behaviour and nepotism because no financial information is released.
Odd or suspicious explanations in the supplemental information at the end of the return.
This is hardly bulletproof since there can be fraud, but I think it is a good place to start.
guidestar requires a free registration for access to tax returns but over several years I have never been spammed or otherwise regretted registering.
If you're talking serious money, consider visiting. It's a tax deductible expense IIRC. If the charity is local, consider volunteering.
HTH