The legend of the Grail is exactly that. The Bible says nothing about Jesus' blood being caught in a cup. The only mention of a cup is during the Last Supper, which is the only true statement about the "grail" in IJ:LC. The look of the cup in the movie is consistent in design; the gold glaze on the inside (which was either just incidental or meant to be an effect of Jesus' blood) would have been unlikely.
It is extremely unlikely that the cup used at the Last Supper would have been anywhere near Golgotha. It belonged to the man who owned the house in which the Last Supper took place, which the Disciples were led to by an unnamed water-carrier whom Jesus told them to look for upon entering Jerusalem. For the next two and a half centuries after the Crucifixion, until the Edict of Milan in 313, the Romans did everything they could to stomp out any mention of any other Son of God besides Caesar. The cup used in the Last Supper, if ever identified as such, was likely destroyed, and in any case virtually all scholars agree it has been lost to time.
The majority of "Actual Grail Lore" is in Celtic and English myth, and states that Joseph of Arimathea took the cup to the British Isles, where it remains to this day in the care of faithful guardians (the Knights Templar). So, the path beginning in Iskenderun (Alexandretta) is wildly inconsistent with Grail lore (it's on the complete opposite side of the old Roman Empire from where the Arthur legends and older works say it should be). That would mean pretty much everything else is completely inaccurate; the knights trying to get back to Rome would have gone through Genoa instead (Venice is on the opposite side of northern Italy), The first marker being in the Middle East, the path of the Grail leading to present-day Jordan, etc etc, all total hogwash both from Biblical and Arthurian sources.