I've found a customer operating as a Sole Proprietor when it appears they should be a partnership.

Missouri allows sole proprietors and general partnerships to operate without state registration. Missouri also allows husband/wife sole proprietorships.

In this case, I've located a loan memo that indicates that the business is owned 2/3 by the husband and wife and 1/3 by a son. From the research I've done, this makes it a partnership.

I'm wondering how much I should push the officer to get them to change the way they are organized and if they will not change (or if the officer is unwilling to push it), what are the risks to the bank?

what are the risks to the bank?

You haven't even begun to tell us what type of relationship you have with them and how it is currently documented. How can we judge any risks?

Both deposit an lending relationships.

CIP is completed on each of the individuals: DLs, tax returns and credit reports on each of the three.

As indicated, there are no state registration requirements for the sole proprietorship, but we do have a copy of the business license from the city in which they operate. We also have confirmed that business income is reported on schedule C of the personal tax returns of the husband/wife.

This is going to come down to the fact of whether or not they are organized in a manner required by State law. If you have a loan with them, then you need to visit with your legal counsel to make sure that it has been created and documented in a manner that binds the parties properly to the loan.

As a side note:the business is owned 2/3 by the husband and wife and 1/3 by a son.

We also have confirmed that business income is reported on schedule C of the personal tax returns of the husband/wife.

This doesn't make a whole lot of sense. I'm not sure of any arrangement involving three people that would not require Form 1065.

Your borrowers need some legal advice about formalizing their business arrangement. They're just kind of making things up as they go along; e.g. saying its a partnership, but taxing the income to Mom and Dad and, possibly, paying junior a salary. If one of them dies or mom and dad get a divorce it will be a mess.

I don't find that Missouri has enacted the uniform partnership act i.e. if there is no partnership agreement you did not make a loan to a partnership regardless of what the memo says. Depending on the wording in your documents, it's likely that you have a loan for which each individual is jointly and severally liable. That's also not smart from their point of view.