Sure enough, she moves in a dog without permission.

A blind person with a seeing eye dog wouldn't have to have permission to stay at your rental.

She invited them in without permission.

While he was working at the house on his estimate, a random guy showed up with some tools and said that his "landlord" rented this house to him and gave permission to store his tools at the garage (mind you, the property has no utilities and needs a complete rehab!)

We have a property with multiple judgement liens from an old owner, but that owner is refusing to give us permission to contact the state to get the liens paid and cleared.Our attorneys are suggesting an expensive and time consuming quiet title action, is there any other way???

Quote from @James Liess: My lease agreement states that I have the permission to mark at the property and show it the potential renters during the last 30 days of a tenant's lease.

Did you have permission to enter the premises? 

An owner, lessor or agent of any riding stable, rodeo ground, training or boarding stable or other private property that is used by a rider or handler of an equine with or without the owner’s permission is not liable for injury to or death of the equine or the rider or handler. 

Written permission from the Landlord is required if any guest remains for more than 10 consecutive days or a total of 20 days in any 12-month period."

Sounds like you have one tenant who skipped out on you (or sublet the unit without your permission) and the current occupants are squatters.