The intended purpose for laying down plastic is to retard the transmission of soil vapor (which is in almost all soils except in extremely arid areas, and inexorably rising due to changes in barometric pressure) from coming up into the basement space. The fact that you are using a dehu means that you have a perceptible soil vapor problem (at least that's why you are paying the electric co. to run the dehus, which is comparable to running an A/C, in some cases). Note however, that I said retard, not completely prevent the rising of soil vapor into the basement atmosphere. Nothing I know of will completely keep it out. Because we now have a goal of sealing up our houses in the name of energy savings (and have modern, and different, whole-house heating systems) rising soil vapor can get stuck within the building potentially causing damage to the structure or contents or residents, if mold develops. Of course your house, like mine, was built with long-tested systems that did not expect, or require, the house to be as hermetically sealed as we sometimes try for these days. In 1857 the vapor was a-rising just as it is today, but it was exiting the building much more easily. Two other factors: people lived and worked at home and were more likely to be aware of and able to adjust the basement openings during the day, promoting additional passive ventilation to remove the moisture. And they may have highly prized that very same moisture if they stored food in the basement. Of course they also didn't have nifty stuff like cross-linked plastic molecules made into cheap (if you don't take into account any off-stream environmental costs), easily laid-out rolls of plastic to put to use, either. Soil vapor is also coming from the basement's walls as your inspector noted. But blocking that moisture is as hard as, or harder, than blocking the soil vapor. If you had thoughts of converting your basement to modern uses (family room, media room, exercise parlor, etc.) you may be disappointed as this is rarely successful in old houses such as ours. So the remaining issue seems to be: how tight is the house above the basement, and how might that tightness be interfering with the house's natural ventilatory patterns. (I think of it as how the house is "breathing", albeit in a passive way.) And of course, it also depends how much more you may be planning to do, in the name of energy conservation, to further tighten up the house. You have run smack into one of the central dilemmas of old-house care: how do you integrate (without doing damage) modern building and energy standards with a structure that was designed and built to support a completely different system? Solving one problem can easily create a new, perhaps more difficult to manage, unforseen issue. There are many opinions and oxen-to-be-gored in this arena. As a practical matter, if you want to lay down plastic (though I recommend special-purpose materials intended for vapor retardation instead of construction poly) and can seal it well with tape where sheets are overlapped, and along the bottom of the walls, you can susbstantially reduce the amount of rising vapor within the basement cavity. But you should know there are some who posit that doing so will shift this moisture (perhaps with damaging consequences) to adjacent soil spaces, including under and in the immediate, exterior vicinity of your foundation walls. This (according to some) may super-saturate the soil, disturbing the necessary firmness and creating settling or susidence problems. Does it? I surely don't know, but it does create - over time - a very moist soil under the plastic. (You can test this by laying a yard-square scrap of plastic on the dirt floor and see what happens.) Others recommend various systems of forced, or air-pressure augmented passive ventilation to remove the moisture laden air from the basement before it can rise into house interior and replace it with (theoretically) drier exterior air. This method has the advantage of not monkeying around with existing soil mositure states, but it is complicated, and may take personal attention to adjust during each day and/or electricity to run. If you have just purchased this house, I think you should observe the ebb and flow for a while (at least a calendar year), as you think about this. And keep the issue in mind as you contemplate any further sealing and insulation projects. It sounds as though the dehus are keeping things in check, so nothing (except cost of power and fuss of removing condensate) is lost by taking a go-slow approach. And by all means, test for radon if you have it in your area. (Your local or state health department is a resource on this.) An upside of the necessary ventilation to control radon can be a reduction of basement moisture since the gas and at least some of the air vapor are removed at the same time.

You could try heating up the tape, but if is pulling off the paint underneath it, then that really could mean that the paint underneath it is not adhered well. This is really one of the reasons why we don't tape walls....you never know how well that paint is stuck because you never know what it was painted with initially. Heating up the tape could minimize the damage, but it is likely that you are going to have to patch the damage and repaint....or you could try touching up if they left you some extra paint.

The drywall is secure. I have no idea why they pulled the original drywall out, but it was not a leak - if it were, the area right under the window would have been the worst. This is a section about 4' long from the floor up to about 3" below the window sill. I assume somebody kicked a hole in the wall there or something. It may have been cracked, or otherwise damaged, but there is no sign of any water damage. Had I needed to remove a section of drywall like that, I'd have removed the ENTIRE section all the way up to the sill - then there would have been no need to tape it, at least not along that top edge. They must have taped it along the vertical seams since all that looks normal. However it certainly sounds like this is beyond my skill set, and certainly outside of the time frame I have to get things done around here. I don't have 3 days to spend on this - especially when its almost certain to take me much longer and/or that I will have to repeat the process trying to get it right. It'll just have to stay the way it is unless the magical wallboard fairies fix it for me one night, LOL! I figured that would be the case. Sadly. Thanks for the help.

Why is this even in the landscape design forum? I'm sure the OP won't listen but add another vote against landscape fabric and rocks. The fabric will eventually break down and create a perfect environment for weeds. The rocks will eventually get clogged with dirt and silt and look ugly. It may be 3 years or 5 years but someone will eventually cuss you as they remove the mess.