Scholars who express doubt about the authenticity or reliability of specific passages in Josephus's writings, particularly his mentions of Jesus (known as the Testimonium Flavianum and the reference to James), include:

Richard Carrier: An independent scholar who has published research suggesting the entire Testimonium passage may be an accidental gloss by a Christian hand.
Philip Davies (deceased): A Professor of Biblical Studies who publicly argued that doubting historicity based on Josephus was a respectable academic position.
Raphael Lataster: An independent scholar with a PhD in Religious Studies, who has presented peer-reviewed assessments explaining his doubts regarding the historicity of Jesus and by extension the Josephus passages.
Ken Olson: A scholar who has argued that the version of the Testimonium Flavianum found in Eusebius is the source for all later manuscripts, suggesting a potential interpolation after Josephus's time.
Robert M. Price: A New Testament theologian and independent scholar who views the Testimonium as entirely inauthentic.
Thomas L. Thompson: A retired Professor of Biblical Studies who has expressed doubts about Josephus's mentions of figures relevant to the Bible.
Alice Whealey: A scholar whose work on the Syriac and Arabic versions of Josephus has been influential in dating the existing manuscripts and understanding potential interpolations.