As you can see, your chances are extremely high that that will come back and bite someone down the road. That's why I've always leaned on the side of an "estate sale" for situations such as yours. With an estate sale, all unwanted/unneeded items are sold by the estate, and any and all proceeds from the sale go to the estate. While it does have a tendancy to lengthen the probate process, it does make it easier when making distributions to multiple heirs of the estate. Cash is much simpler to divvy up, than physical property is.
When items are donated, be it from the estate before the completion of probate or by the heir after they have legally acquired possession and probate is closed, it can be a lot more paperwork and a lot more expense involved in providing the necessary documentation trail to justify the value of those items donated. Without that proof, should one be audied on it there is the possibility that the IRS will reduce the value allowed, and in some cases eliminate it completely.
I would suggest that if it's not to late, reschedule the pickup for a later date. Then either hold an estate sale, or do the paperwork and legwork necessary to justify the value of what gets donated. Either way, you can expect some expense to be incurred to do that. If the items have not yet been legally transferred to heirs from the estate, then the estate can pay those expenses. Otherwise, the new legal owner of the property to be donated, incurs the expense of proving value, if any.
