It might also become harder to evict the tenant if need should arise when the tenant has already paid rent.

(I'm not a lawyer, but I have a good grasp of history.)As someone else pointed out you can put just about anything in a contract but its enforceability is another matter entirely.If you're just trying to reduce the business risk arising from a lawsuit, just be sure to be properly ensured.

You can just give 30 days notice (normally) for changing any rules if any problems arise, and raise the rent, etc., without having to wait until the end of a lease.So, I'd suggest you just have them sign a new month-to-month agreement to start with. 

I never had this situation arises for an applicant to add extra occupants AFTER I accepted the application that listed one occupant.

What would be some of the problems that may arise with trying to rent rooms in a property that has been illegally converted into a duplex?

Your cash flow cannot afford to fix all of the issues that arise in these neighborhoods.

Anyone could find a way to replace a riser.

When problems arise, worst comes to worse you sell and can reinvest in closer to home markets with better rental/cashflow numbers and you will be all the wiser.  

The situation of under market rents arises from the fact that the vast majority of landlords are in it as a hobby.

There are two ways this can arise; an equitable servitude (which must generally be in writing) or an easement.