Our band booster organization is incorporating and will seek 501(c)(3) charitable recognition. The officers insist that no provisions for an annual audit are necessary; they believe that having several of the members review the books is sufficient. Is a 501(c)(3) not required to have an external audit?
Not under federal tax law. The Form 990 tax information return asks whether you have an audit and gives you space to reconcile differences in numbers prepared for financial accounting purposes and for tax reporting purposes, but the IRS does not require an audit of any charity, regardless of size.
If you are required to register to solicit charitable contributions in your state (or others where you solicit), there may be a state law requirement for an independent audit, but the threshold for such a requirement is usually several hundred thousands of dollars of income or contributions. A local band booster organization seems not likely to be large enough to be required.
You ought to be sure that you have people who understand accounting to do the review, and it is certainly a good idea to produce a financial statement that can be shown to your donors if they ask.