If it's remediated then it is essentially gone unless the moisture comes back (that's the more serious problem; is the water leakage fixed?).

.-  Basement has an obvious moisture problem.-  Subfloors are saturated with moisture at some parts, leading to wood rot, fungus/mold, and obvious safety issues.-  The floor unit above the basement's problem site has a concerning issue with floor sloping/alignment.

How do experienced investors view things like water/moisture in the basement of a property?

A simple way to know that the members have been dried enough is to invest in a non-intrusive moisture meter and gauge the moisture content.

It backs to rt 59 and is very loud and I heard there is issues with the stucco and moisture that has got behind the walls.

We recently ran into an issue where the floor joists in the house were rotting due to moisture issues under the house where there was no moisture barrier from the ground and the house being built so close to the ground. 

The roof has been repaired, but there was no carpet, and there was some moisture damage in the ceiling and the house smelled like cigarette smoke.

I got the inspection done the other day and discovered quite a few issues that should be addressed ASAP:-new chimney: the bricks are falling odd-cracked asphalt on one of the front steps-one of the floor joists need to be replaced-some previous foundation settlement issues: the inspector suggested getting a structural engineer to come and look at that-some moisture damage that will be taken care of by the seller-it appears there might have been some termite infestation in the past: the inspector suggested getting a terminate radon inspection done-new garage for needed as the current one couldn't be opened-new ceiling in garage needed as part of it was ripped off, exposing wiring: could lead to a hazardOther than that, a few minor things here and there like replacing a floor tile here, etc.Here's the thing: I'm an out of state investor and was looking for something that didn't need much work.

I have had a tarp put in place to stop the moisture from getting in.  

I would suggest a newer build [1998-up] like a subdivision "vinyl village" home to purchase.These will cost a little more than an older home with the same rent but are much newer, typically on a slab [no moisture issues to deal with] and are easy to rent and/or sell in the future.One downside of this type of home is that most good markets [Indianapolis included] have been invaded by the Wall Street Hedge Funds and they have or are buying up this product at record rates.