According to our lease agreement, "... in the event of early termination by Tenant prior to completion of the original term of the Agreement, Tenant shall also be responsible for lost Rent, rental commissions, advertising expenses, and painting costs necessary to ready Premises for re-rental.

Boris, if you don't own the duplex yet, why don't you have the seller deliver the property to you vacant - and let him to the termination of lease? 

Yes if you are unable to find a buyer you are contractually obligated to purchase the house unless the seller will let you out of your contract or if you have a valid reason for termination.

Then document it your notices like crazy - with pictures if you can - and let them know they are in breach of the lease, thus the lease can be terminated upon proper legal notice.

I have a good tenant that would like to terminate his lease early because of a new work location.

Lots to think through, but I'd start with thinking about your local market and if your goals are primarily short term or long term in nature. 

Notice to terminate must be given prior to the beginning of a rental period, prior to the first of the month.

Left some junk stuff behind the house. 4)Tenants kept asking me if I could terminate my lease earlier since they moved out (I guess they had to sign up another lease with the other landlord before this lease is over).

Could be as small as a dead battery in a smoke detector in the middle of the night (no guest wants to hear beeping while they are trying to sleep), guests can get rowdy and disturb neighbors, I have even had guests that insisted upon having someone meet them face to face when they arrive.

fresh batteries in all.