The properties are expensive (low cap rate), but the property and rent appreciation have historically been outstanding. 

To my pleasant surprise she admitted she herself just learned that there is $20,000 of outstanding taxes on her property!

I have 4 outstanding mortgages in rentals ranging from 3.75% to 4.125% on 30 year notes. 

You will want to do a title search to make sure there are no other outstanding liens.

(read as:  still outstanding)A 30 year mortgage is 360 periods of 30 days each.  

The refi is just the outstanding balances.

How can I check if there are any city orders against a property, or outstanding liens?  

That means that if the lender seizes and sells  the property and the sale price doesn't cover the outstanding loan amount, the lender can't come after the borrower's personal assets to make up the difference. 

How difficult would it be to work with a lender to buy a third home (with outstanding credit) We have  no late payments on mortgage, long term job stability.

Outstanding loan amounts will be considered and the ability to pay, if both are knocking down good incomes you may not have an issue, if one is relying on the income of a spouse, you're in a different boat. :)