., you definitely want to do this for higher end rentals because people expect modern conveniences and it will get you top rent for the place.

They also help 'sell' the place to the potential new tenant, talking about the lifestyle or conveniences that comes with the house, and it seems to help minimize the vacancy period.Does anyone else do this?

You cannot just put in whatever rules you want to suit your convenience.

I don't think they are particularly unreasonable for a careful landlord, but I think the quality of tenants in the area might not be so great to begin with and including these details upfront makes me come across as a tough landlord:  Application: Background check ($25) Past landlord, employer, and personal referencesLease Points: Initial lease term is 8 monthsMonthly rent of $865 due on the 1st of each monthRefundable Security Deposit of $865Pet Fee (if applicable) of $200 upfront and additional $25 per monthOptional FrontPoint security system for $100 upfront and additional $50 per monthTenant pays for water, gas, and electricityRefrigerator and range oven includedWasher, dryer, dishwasher, and microwave not includedNo smokingAbsolutely no illicit drugs or other illegal activityTenant responsible for damages beyond ordinary wear and tearTenant required to purchase renter’s insurance before move-inNo assigning or subletting without landlord’s permission* The above list is intended only for purposes of convenience and is in no way incorporated into or comprehensive of the Lease Agreement, nor is it binding.

The majority of my tenants are 30-ish so they will like the on-line convenience.

It depends on your present lease agreement, tenant and condition of the property.....it may work in your favor to show it early if the current tenant has maintained it well and is agreeable to well screened serious  potential tenants viewing at a convenient time.

While waiting for a convenient time to pick it up, it was returned to sender. 

You can put aside an hour a couple times a week and communicate that to the prospects, they can choose from times convenient to you.b: when a prospect visits an open house and sees a crowd of others, it gives them a sense of competition (more urgency to get their application in, crowd validation that it is a good place to live).c: safety.  

Only thing is new tenant has yet to live there a full day and is already expecting me to let in his son, etc.As much as I find it convenient to deal with contractors and prospective tenants living on site myself, one downside I'm starting to find is these strange little requests the new tenant makes.

Due diligence should not be altered for the convenience of the tenant.Good on you for finding a cash flowing rental property