But the water went only partially into the living area - we may have been able to salvage that part of carpet if not for the tenant's significant damage to it (pet stains and ground in dirt stains.)

So that if I get a house with several water stains in the ceiling and I don't know where they are coming from I would add a 20% buffer to my plumbing and drywall work in case I got to go fishing for leaks once I start running water.On the other hand, is there really a lot of risk in say, paint or appliances or landscaping?

You can probably see where the stains are anyways, if not get a UV light.

In both units, the bathroom tubs leaked through to ceiling below and the downstairs showed water stains.

I will be using a 30 fixed rate mortgage and putting 20% down.After I close, I will be doing the following renovations: Refinish/stain the original hardwood floors which appear to be in pretty good shape; new interior trim; renovate full bath (tile floors, tile shower surround, new toilet, new vanity, towel racks, etc); paint interior; new interior light fixtures; minor landscaping; new interior doors; new closet shelving.  

Then stained concrete popped in my head.

Debating between refinishing what is there of just buy new to put down for less time and have the wider plank look.Didn't know to do hardwood first and then put sheet down to protect when the carpet people come in or do new carpet and then put hardwood down after that is upfront.If I put carpet first I was thinking when they re-stain hardwood it might get some on the new carpet versus the old I wouldn't care as it is being ripped up anyways.I will probably go for plush carpet with a nice thick pad.

You could walk in and find that they stained carpets or have mold in the bathroom or who knows what else.

There appears to be some stains indicating seepage.We just did this kind of foundation repair on a house with steel beams 6 ft oc with an interior moisture barrier and an interior drainage tile with a sump.  

Maybe try a solid stain or deck paint that is designed to hold up under tough conditions.