I took some pictures of the effect area to try and eyeball any leaks, but heck I'm no plumber.

Pictures Sell!

Eventually the oil supplier will come periodically, fill up the tank, charge the tenant directly, and I'll be out of the picture, but since I've already paid for the oil in my tank I would want to charge the tenant for what he's using.Any advice on the subject would be appreciated.

You may not have a clear picture.

Landlords- Would you consider it a valuable service to receive a periodic report, summarizing the condition of your rental property, along with pictures, right to your inbox?

I've offered pictures to landlords & to bring my dogs to meet the landlord to prove their temperaments & tried to reassure them that they're both house broken, crate trained, supervised 100% of the time we're home or in kennels when we're not, and not destructive even if they weren't supervised. 

I don't think it's quite as gloomy as you paint the picture.

The financial industry, at least the traditional large financial industry, wants to see a lot of data and be able to ascertain with reasonable certainty your long term delinquent rent rates, eviction rates, fees, rent increases, operating costs, and your (or your company's) personal financial picture and stability.

I have some before, during, and after pictures of a rehab in a gallery:http://www.biggerpockets.com/galleries/show/16

This could be costing you hundreds to thousands of dollars per month (depending on your situation of course), which in the big picture will net you less money in the long run.