Your question actually has 2 issues in it.
1 - He is on the ex's mortgage but not on the deed.
Worst case scenario is that she stops paying and he has to start, even though he doesn't own any interest in the property.
2 - "his farm is still mortgaged againt his exwife's home"
Do you mean that part of the collateral for the ex's house is the farm he currently owns?
If so, the worse case scenario if she stops paying and he can't afford to pay is that he loses his farm. Even if she personally defaults he can't even force the ex to sell the house to try to negate the loan because he doesn't own the house.
What needs to happen next is combing though the divorce papers.
If the decree says she needs to refinance as a condition of keeping the home, then he can pursue it. If she is unable to refinance, then she will probably have to sell.
If the divorce decree did not require her to refinance the home into her own name only, your fiance has no legal grounds now to make that happen.
Honestly, if everything is going smoothly now and they have an amicable relationship, another option is to just let things stand as they are. He should consult a lawyer about any ramifications to doing that.
As for your marriage, have a pre-nup so that what's yours remains yours, and his remains his. That way you won't personally be stuck with any financial burden if things go south.