Curb your enthusiasm and be a skeptical investor.

Of course I could advertise and take applications while under construction.Second question is how would you determine your absolute best offer price on a building that is 100% vacant, with competing units in the area that are newer and have much more curb appeal?

That means that it is really a curb you are jumping off, it isn't as scary as it seems.

What they lack in curb appeal they make up for in steadfastness.

Do I have to go to eviction court, or can I just ask the sheriff to come put his stuff on the curb?

Let's set aside the obvious answer of, "Don't buy the rental if you can't see the inside and/or talk to the tenants first." because on curb offers you aren't allowed inside until you have an accepted offer.  

The house needs asbestos siding and wood lap siding striped and new siding put on in order to have good curb appeal.

Curb appeal can work wonders and can be done cheaply.

I have found it typical for Owner's to pay for landscaping ($60-$100/mo) if they care about the curb-appeal of their rentals.

Next I would do a google street tour of all the comparable sales to compare how the street looks and the curb appeal was for each property.