Just one or two observations before I feature some specific pieces in a later entry: a small number of bone fragments are on the right and beneath them is an encrusted nail-like object (which I wouldn't normally bother with but it is quite long and slender); the majority of the sherds are unglazed; of the glazed pieces there is one that is splash glazed, one fully olive-green glazed and one partially dark green glazed with grey fabric.
In the centre of the display, the largest sherd is exciting! It has signs of finger indentations at two of its tips with accompanying fingerprints. It is quite flat so I cannot make out what kind of artefact it comes from.
I think that the pieces come from a range of eras but I don't want to prejudge the expert opinion.