Over 40 years later, and people still get this wrong. The "Brian" character in the movie is not "mistaken for Jesus Christ," although he is erroneously identified by some as being the long-awaited Jewish Messiah.
In fact, Jesus is respectfully portrayed in the movie -- preaching the Sermon on the Mount -- although some of the more thick-headed among his audience don't get his message. The actor playing Jesus, Kenneth Colley, is better known for his turns in a couple of the early Star Wars movies.
Oh, I suppose that in the opening scene, where the Magi at first show up at the wrong stable, it might be said that the newborn "Brian" is "mistaken" as the newborn Jesus, but that error is quickly corrected.
Something about “blessed are the cheese makers….”