"The sacred books which contain the prayers recited or chanted during the [Mithraic] survives, the ritual on the initiates, and the ceremonials of the feasts, have vanished and left scarce a trace behind...[we] know the esoteric disciplines of the Mysteries only from a few indiscretions." (Cumont, Franz. The Mysteries of Mithra. New York: Dover, 1950.152)
( Roman Cult began after Jesus life
Our earliest evidence for the Mithraic mysteries places their appearance in the middle of the first century B.C.: the historian Plutarch says that in 67 B.C. a large band of pirates based in Cilicia (a province on the southeastern coast of Asia Minor) were practicing "secret rites" of Mithras. The earliest physical remains of the cult date from around the end of the first century A.D., and Mithraism reached its height of popularity in the third century.(Ulansey, David. Cosmoic Mysteries of Mithras (website)
No Continuity between Ancient Persian past and Roman Cult
Throughout most of the twentieth century Franz Cumont so influenced scholarship that the entire discipline followed in the wake of his assumption that the Roman cult was spread by the Persian cult. In the early 70's David Ulansey did for Mithric scholarship what Noan Chomsky did for linguistics, he totally redefined the coordinates by which the discipline moved. Ulansey showed that the Roman cult was not the continuance of the Persian cult, that there was no real evidence of a Persian cult. He showed that the killing of the great comic bull which latter became the major event in Mithraism, and the parallel from which Jesus Mythers get the shedding of blood and sacrifice, was not known in the Persian era. This was be like showing that the story of the Cross was not known to Christians in the first century. The major likeness to Christianity and the central point of the cult of Mithraism was not known in the time of Christ, in the time Paul, or for at least two centuries after:
"There were, however, a number of serious problems with Cumont's assumption that the Mithraic mysteries derived from ancient Iranian religion. Most significant among these is that there is no parallel in ancient Iran to the iconography which is the primary fact of the Roman Mithraic cult. For example, as already mentioned, by far the most important icon in the Roman cult was the tauroctony. This scene shows Mithras in the act of killing a bull, accompanied by a dog, a snake, a raven, and a scorpion; the scene is depicted as taking place inside a cave like the mithraeum itself. This icon was located in the most important place in every mithraeum, and therefore must have been an expression of the central myth of the Roman cult. Thus, if the god Mithras of the Roman religion was actually the Iranian god Mithra, we should expect to find in Iranian mythology a story in which Mithra kills a bull. However, the fact is that no such Iranian myth exists: in no known Iranian text does Mithra have anything to do with killing a bull." (David Ulansey Mithras Mysteries).
Mithraism Emerged in the west only after Jesus' day.
Mithraism could not have become an influence upon the origins of the first century, for the simple reason that Mithraism did not emerge from its pastoral setting in rural Persia until after the close of the New Testament canon. (Franz Cumont, The Mysteries of Mithra (Chicago: Open Court, 1903), 87ff.)
We Don't know what any of it means.
"No one can be sure that the meaning of the meals and the ablutions are the same between Christianity and Mithraism. Just because the two had them is no indication that they come to the same thing. These are entirely superficial and circumstantial arguments." (Nash, Christian Research Journal winter 94, p.8)
Mithraism was influenced by Christianity
a) Roman Soldiers Spread the cult.
Roman soldiers probably encountered Mithraism first as part of Zoroastrians when they while on duty in Persia. The Cult spread through the Roman legion, was most popular in the West, and ha little chance to spread through or influence upon Palestine. It's presence in Palestine was mainly confined to the Romans who were there to oppress the Jews. Kane tries to imply that these mystery cults were all indigenous to the Palestinian area, that they grew up alongside Judaism, and that the adherents to these religions all traded ideas as they happily ate together and practiced good neighborship.
b) Mithric Roman Soldiers Influenced by Christians in Palestine
But Mithraism was confined to the Roman Legion primarily, those who were stationed in Palestine to subdue the Jewish Revolt of A.D. 66-70. In fact strong evidence indicates that in this way Christianity influenced Mithraism. First, because Romans stationed in the West were sent on short tours of duty to fight the Parthians in the East, and to put down the Jewish revolt. This is where they would have encountered a Christianity whose major texts were already written, and whose major story (that of the life of Christ) was already formed.
There is no real evidence for a Persian Cult of Mithras. The cultic and mystery aspect did not exist until after the Roman period, second century to fourth. This means that any similarities to Christianity probably come from Christianity as the Soldiers learned of it during their tours in Palestine. The Great historian of religions, Franz Cumont was able to prove that the earliest datable evidence for the cult came from the Military Garrison at Carnuntum, on the Danube River (modern Hungary). The largest Cache of Mithric artifacts comes form the area between the Danube and Ostia in Italy." (Franz Cumont, The Mysteries of Mithra (Chicago: Open Court, 1903), 87ff.)
3) Mithraism was not Christianity's Major Rival
Mithraism, The Ecole Initiative, http://cedar.evansville.edu/~ecoleweb/articles/mithraism.html
Mithraism had a wide following from the middle of the second century to the late fourth century CE, but the common belief that Mithraism was the prime competitor of Christianity, promulgated by Ernst Renan (Renan 1882 579), is blatantly false. Mithraism was at a serious disadvantage right from the start because it allowed only male initiates. What is more, Mithraism was, as mentioned above, only one of several cults imported from the eastern empire that enjoyed a large membership in Rome and elsewhere. The major competitor to Christianity was thus not Mithraism but the combined group of imported cults and official Roman cults subsumed under the rubric "paganism." Finally, part of Renan's claim rested on an equally common, but almost equally mistaken, belief that Mithraism was officially accepted because it had Roman emperors among its adherents (Nero, Commodus, Septimius Severus, Caracalla, and the Tetrarchs are most commonly cited). Close examination of the evidence for the participation of emperors reveals that some comes from literary sources of dubious quality and that the rest is rather circumstantial. The cult of Magna Mater, the first imported cult to arrive in Rome (204 BCE) was the only one ever officially recognized as a Roman cult. The others, including Mithraism, were never officially accepted, and some, particularly the Egyptian cult of Isis, were periodically outlawed and their adherents persecuted.