What are the rules on making financial reports public in a 501 c3 Organization

The 501C3 must file a Form 990 tax return with the IRS, which is made available to the public. You can search for the Form 990 for a particular organization here: GuideStar nonprofit reports and Forms 990 for donors, grantmakers and businesses

Here's a good article on how to check up on a charity:
Check Out Your Charity

In addition, any reputable 501c3 should publish an annual report that they make available to its constituents.