How important is it for a Mac admin account to be associated with an Apple ID My wife and I have an iMac. We each use standard user accounts associated with our respective Apple IDs. We also have an administrator account that is not associated with an Apple ID.

What problems, if any, could the admin account not using an Apple ID cause? Should we add one of ours to it?
This association is purely optional. You don't need an AppleID or an iCloud to manage your Mac and as long as you're the original purchaser and have proof of purchase, you can lock the firmware, iCloud Activation Lock and take your Mac to Apple and they will unlock it for you.

The only reason to put your admin account into iCloud is if you want to let that other password for iCloud / AppleID unlock the Mac, store/sync keychain items in iCloud or use other features of the AppleID.

Choose good admin passwords on your Mac, write them down in a safe place (1Password, bank safe, place where you can get to if you forget a password) and you'll protect the admin password and your Mac.