Our story about the closure of a food bank ministry prompted a Facebook comment warning donors to make sure they know to whom they are donating.
I wanted to mention the Evangelical Council on Financial Accountability in this context. I was on the board of a domestic missions group at the time it joined ECFA, and was on that same board a few years later when we had a fiscal crisis, and I can assure you that ECFA membership is a good indicator that a faith-based charity has its house in order. ECFA has been around for decades, but it got stung by some of the televangelist scandals in the mid-1980s and really strengthened its process, so that by the time the group I was involved with joined, 10 or 15 years later, it was a lot more difficult to gain and keep ECFA membership.
In order to join ECFA, a non-profit organization must subscribe to basic Christian doctrines and must agree to a rigorous set of standards for governance and financial management. The non-profit must have an active governing board, must be audited regularly, and must make copies of the audit available to anyone who asks. ECFA gets a copy of the audit and will get involved if there's any hint of irregularity.
There are rules governing conflicts of interest, and rules governing use of donations. (If you give money for the building fund, for example, it has to be used for the building fund, not diverted to some other line item, however worthy.) If outside fund-raisers are used, they have to be paid fee-for-service, not based on a percentage of what they raise, since that system sometimes leads to abuse.
As you decide which faith-based charities to support, I encourage you to ask them if they are ECFA members or look them up at ECFA's web site, http://www.ecfa.org. That's not to say that there's anything wrong with a charity which isn't involved in ECFA; some smaller charities, especially, might have a hard time meeting its entry requirements. I currently serve on the board of a small foreign missions group, with no full-time employees, and it would probably be hard for us to join ECFA.
But I believe ECFA membership, when you do see it, goes a long way towards reassuring you that everything is above-board.