Does a permit need to be pulled for a single stair way?  

The stairway to the 3rd floor is entered from a doorway in the guys bedroom. 

9.43.010 COMPATIBILITY IN RESIDENTIAL ZONESNo person shall construct any dwelling, accessory building, or structures, improvements, patio covers, roofs, balconies, decks, porches, terraces, exterior steps or stairways, walls, fences, antennas, spas, swimming pools, or make any additions to, or modify, any structure, or install a new roof on any structure, on any parcel in a residential zone in the City for which a building permit is required unless the resulting construction is found to be compatible with the neighborhood within which it is located.

One rental house automation I will add is "if it's between sunset and sunrise and the driveway motion sensor goes off, turn on the stairway, main door, and under house lights, then turn them off 10 minutes later". 

For the new multi-family (and this was the same Texas storm @Roy N. references) we put salt on two steep stairways and in entrance ways.

The delivery guys offered to be back next day, but the President changed his mind to let them move using the stairway instead of eleavtor.

There is an exterior entrance plus a stairway to the upstairs with an exterior door at the top of the stairs.  

Even if you are talking infants, what if one crawls off of a stair way, or eats leadbased paint chips?

Odd floorplans, tiny "bedrooms" with no closets, stairways to nowhere, unuseable fireplaces, all affect the marketability of your rentals, and the type of tenant you will get.

The owner is the largest tenant with 2,120 sq ft, another tenant has 1,606 sq ft, balance (3) are all less than 400 sq ft, vacant office of 350 sf. with the balance being common elements, corridors, stairways, elevators, bathrooms, kitchen, etc.Gross rental income per the listing agent is $108,660, expenses are $41,225 annual condo fee (CAM) which includes electric, water/sewer, janitorial and property management, the estimated new property taxes are $15,500, and insurance approx. $2000.All tenants' leases are 1 year and/or have less than 1 year remaining.The property was purchased by the seller in 2011 for $350,000.