Two areas that all clubs need to be aware of are licensing and insurance. Unfortunately, these have often been overlooked.
Your licensing needs will vary depending on the type of club you have, and the venue. It is often not well-understood that you must have a performance license for any music played in public, and this includes square dance groups. There are two primary companies that provide this type of licensing:
Legally, you cannot use your own records or MP3s to perform or teach dancing in a public place, such as a square dance club, unless you have obtained a performance/teaching license.
If you have a club caller, may not need to purchase a license. You should check that your caller is properly licensed. (Most callers have their own license with BMI/ASCAP that covers them for teaching and calling dances at your venue). Some venues may have their own licensing requirements, so you should also check with them before purchasing licenses.
There are organizations that have negotiated discounted licenses for callers/clubs. CallerLab for example has more information here.
It's an unpleasant fact; people have accidents, and people sue. For these reasons, you need to ensure you are properly covered for liability insurance. While it may not be your fault that a dancer tripped on a cable or slipped on some spilled water, your club might still end up having to pay medical costs and damages. Having the right insurance is important to protect your club members from litigation. If your club is a member of a local square dance association, they should be your first stop in looking for insurance information; often regional associations have contracted with insurance companies to secure insurance at reduced rates for their member clubs. Otherwise, search locally for an agent from any of the national insurance companies - they'll be happy to provide you with a quote.
If your club is a member of the United Square Dancers of America, you can also obtain discounted insurance through that organization.