Never do an inspection alone or without their consent if they are occupying or have some stuff in it.  

I consented to do it because he started to threaten me that I misrepresented the property and he can sue me etc.

Obviously a person with a long list of convictions is a no-go, but they usually have the girlfriend or grandma apply anyways and will move in without your consent - lol.But back to the main point - month to month.

Here is a link to my blog about renting out such RE. https://www.biggerpockets.com/member-blogs/12388/86773-renting-real-estate-without-the-owners-consent-isn-t-that-fraudAnd here are links to a couple short videos that discuss the demand, at least here on the West Coast, for places to park RV's.In the San Francisco area, https://www.youtube.com/watch?

So my only remaining question is can one tenant legally terminate a lease for all the other tenants on the lease, or must they all give consent? 

I would have them sign an addendum (like @Max T. suggests) similar to this one:This agreement serves as consent from the Landlord to permit Tenant(s) to attach and use a clothes washer and/or dryer within the aforementioned rental unit under the following conditions:Any damage to the Premises caused by water originating from the washer and/or its connecting hoses will repaired by the Landlord at the undersigned Tenant(s) expense.Tenant agrees to regularly maintain and clean lint/debris from the dryer unit itself as well as attached ducting.

You agree not to install a washer or dryer in your living unit without first receiving our written consent.

My guess is your position will be hard to defend with this type of tenant reaction combined with no written documentation of their consent.  

Here is my current pet disclaimer:No animal or pet shall be kept on or about the premises without Landlord's prior written consent, except any pet that may be listed below.

On top of that I'm not getting full consent from the current tenant.