We're hoping that the sellers will acknowledge responsibility for this, and that they'll have warranties from their contractor or otherwise be willing to pony up the costs, which may be substantial. ($15-$20K). We'll see what they say. At the least, this may well push off closing, since they may want to get a certified mold inspector person out to verify this development.
We've been doing a lot of research, and it seems like mold is present in most basements, especially most basements of old houses. "The American Society of Home Inspectors...estimates 60 percent of U.S. homes have wet basements, and 38 percent run the risk of basement mold." Mold removal companies seem to promote a lot of hysteria on the subject to get people to spend money, but the mold itself isn't likely to be a big problem. There's a specific (rare) type of mold called toxic black mold that is a big issue, but what we have probably isn't that. Mold is actually everywhere, and you, your kids, your dogs all probably are carrying mold around with you. Is okay. Mold is a warning sign in a basement more than an actual problem in itself, unless you have asthma, other breathing problems, or are immuno-compromised in some way -- i.e., I probably shouldn't spend time near the moldy corner of the basement while pregnant, or with new infant.
What we're actually worried about is stopping the wet basement issue from developing further, so the question is whether we want to pay the additional $15-20K that we hadn't budgeted for, to open up the drywall and add the vapor barrier/drains/sump pump that probably should have been installed the first time around, and which are likely to significantly dry out the basement.
Alternatively, we could buy the house and then do what most people seem to do, which is simply redirect the downspouts further away from the house/basement, regrade the land near the house so it's less likely to direct water to the foundation, clean the gutters, and tuckpoint the above-ground part of the stone foundation. This is a much cheaper fix, and the sort of thing that people have to do with any old house periodically anyway. Then wash off the mold with bleach, and watch the situation, to see whether that fixed the moisture problem.
Keep in mind that most of the old houses in Oak Park will have wet basements and some mold. The problem we're having here is that since this basement was redone just a few years ago, we'd hoped that they'd taken care of this then, so we weren't expecting another $20K in costs here, which would take us right up to the edge of our budget, and keep us from buying furniture/repainting/etc. for a few years.