I know that the general claim is "the path of the bullet that hit Kennedy is physically impossible, so there must have been a second gunman" and I know that the consensus is that this claim is wrong, but that's just about all I know.
The magic bullet theory is, indeed, the claim that the trajectory of the bullet was impossible, requiring several turns in mid air, and thus that there was a second gunman.
In reality the magic bullet theory is based on some false premises, and itself ignores some of the critical evidence. As in, if the magic bullet was fired by a second gunman we are short one bullet hole in the car...
Note, the 'magic bullet' was the 2nd (of 3) Oswald fired. The 1st missed cleanly. The 3rd was the head shot that killed Kennedy.
Also, given the range and circumstances, this did not require nor did Oswald demonstrate unusual marksmanship.
Some issues-
Kennedy was shot from behind, why did his head jerk backwards. This is a subtle effect of physics. Penn and Teller (among others) recreated it exactly with a melon. Not an issue.
Bullet trajectory- The Magic Bullet Theory assumes several things there were not, in fact, correct.
The car they were in was not a normal model. It was specifically modified for parades, to show off the important passenger.
As a consequence-
A) Kennedy and Connolly were not aligned front to back. Connolly was closer to the center.
B) Kennedy and Connolly were not at the same height. Kennedy's seat was higher, so the crowds could get a better look.
C) Kennedy was not sitting upright at the time. He had leaned forward to talk to Connolly ('was that a gunshot?')
D) Connolly was not facing forward at the time, he had twisted around to listen to Kennedy.
As a consequence of all of this, there was, indeed a straight line through Kennedy and Connolly, and thus no need for turns in mid air and no actual 'magic bullet'.
Why was the bullet not deformed? Until it ended up in Connolly's wrist, it passed entirely through soft tissue. And the bullet was, in fact, deformed.
Kennedy's as the most investigated murder in world history. And the committee doing the investigation was extremely thorough. There was no conspiracy, no second gunman. There was just a lone man with an opportunity.
Follow-up: when did this theory rise to prominence? Is it just with the film JFK? Or had it been in the public consciousness for a while?
On a somewhat related (maybe it should be in a separate thread) topic.
How do historians handle situations like the recently released trove of documents about the JFK assassination?
10 years from now will historians basically consider all Scholarly works up to this date irrelevant/obsolete because everything published after this year will have so much more source materials to work from?