I guess my biggest problem with the Bahai faith is the doctrine of progressive revelation. Since it includes both Muhammad and Jesus, the concerns I have with Islam pertain to Bahai, it would seem that Bahai faces the same concerns.
I do not believe that Muhammad was introducing a new religion, but trying to bring the Hijaz to dyophysite/Nestorian Christianity. All of the extant biographical information we have for Muhammad dates to at least 200 years after the Hijra, and hadith have not been shown to be historically reliable. I believe the Quran is a pastiche assembled under scholars working for Uthman, based on some sayings of Muhammad, the compiled midrash of Rabbinical Judaism, (possibly) pre-Islamic Arabian poetry, and Christian scripture, liturgy, and apocrypha that were popular in folktales of the region. The Quran’s many references to Mary and Jesus, to me, probably reflect the widespread popularity of Marian devotion among the Christians of the lands conquered by in the 630s and 640s, plus the dyophysite/Nestorian emphasis on preventing a mixing of Jesus’ divine and human natures – which emphasized his human birth through Marian stories.
I think the Quran is a work of genius, both literary, philosophical, and linguistic (involving the invention of classical Arabic script) – but it is not divine revelation. It is doctrine meant to secure the exclusive claims of the Rashidun caliphate to legitimacy – which the events leading up to the First Fitna demonstrate as shaky. In that regard, it’s more like Virgil’s Aeneid, which was written to provide historical and moral legitimacy to the imperial reign of Augustus Caesar.
Christianity faces its own documentary challenges, largely as a result of the Gospels being written as works of theology and/or midrash, with references to historical traditions and now-lost documents (e.g., the Q gospel). However, it is impossible to make the claim that the earliest Christian history is the deliberate product of a single editorial process. If anything, Islam and Christianity face opposite problems: Islam claims to be unified and homogeneous from the time of Muhammad onward, a claim assisted by Uthman’s burning all extant documents on which his compilation was based. Christianity’s earliest documents show a far from homogeneous theological mix. For example, there are christological statements in the Bible that even modern Christians reject (e.g., Romans 1:4 appears to be part of a pre-Pauline creed that Paul cites that say that God adopted Jesus as his son through the resurrection).
It seems to me that the Bab’s teachings, and hence that of Baha’u’llah, are based on the Bab claiming to be the Mahdi. That’s a title borne of Muslim end-times prophecy, so hence my problem…