Can a city in Minnesota force a landlord to evict or remove their tenants due to ordinance or code violations?

The landlord should do it. I can't imagine the landlord would want that kind of attention.*

In a way yes they can, they can pressure the landlord to straighten up whats going on. But the catch is the landlord can't evict without due cause. Some breech of the lease. So the question becomes, are they doing enough to actually be looked at as breaking the lease. Or are they just a pain but still within those boundary's?

What codes or ordinances? If the PREMISES are illegal in some way, the city can force the landlord to bring them up to code, and/or evict tenants. If it is actions of the tenants themselves (noise, etc), the city can only act against the property owner. He CAN use that enforcement to evict his tenants, but he is not required to do so, if he wants to keep paying the fines.

Yes, neighbors simply obey with ordinances. That's simply reality

Yes. Absolutely. I'd be mad at my city for not leaning on the landlord in such a situation.

Most likely the answer is yes. (However in most states they will have to prove the claimed violation) which would mean the neighbors who are complaining about you would have to come to court. 100% right answer check the lease that is what the judge will look at to make there mind up and so should you.