Scholars who are not concerned with lab testing have openly questioned the authenticity of the Jerusalem papyrus, among them some of the most highly-respected archaeologists, epigraphers, and philologists in the world. Part of what drives this doubt may be technical concerns over issues such as whether the script used is what we would expect to find from the seventh century, or philological details such as whether the place name in the papyrus, Naharata, is grammatically correct. But for many, the overarching problem is how the text came to light in the first place.As usual, Moss and Baden give us a good summary of the current state of play concerning the papyrus.
Background here (cf. here) and links.