I'd prefer that you review and agree to my lease and I will get them electronically signed and send you a copy.

Yes- electronic payments are the best way to go in most cases- avoid "check's in the mail" excuses.

From that one checking account you could do the following:1) Use an electronic rent payment solution which allows for rent to be sent directly into that account.

There are self-services for screening, but IMO if you have an agent they should be assisting with the electronic screening and presenting the reports to you to decide, as well as weighing in on what they saw in the report of note.

Legitimate companies do use electronic lock boxes for convenient self-showing, but those systems often require you to register through a site and verify your identity before entering the property

Most cities are now taking submittals electronically and so there is no permit running like their use to be.  

All electronic.

As far as rent I would just make everyone pay electronically that way there is no need to physically collect rent and you can avoid those situations. 

@Peter Morgan if it is an electronic read that meter might not have registered.

The strange thing was, every time I left Los Angeles and traveled a little distance a water heater in one or another building would go on the blink on a weekend and every tenant would scream about not having hot water and it is difficult to find a contractor who can repair most of these new water heaters with all sorts of new electronic circuit boards and gadgets on them.