The main conspiracy points are outlined below. (They are in no particular order).
1) In the Zapruder film, JFK, when shot in the head, lurches 'back and to the left'.This surely must mean he was shot from the front right (ie from the Grassy Knoll) and not from behind from the School Book Depository?
Ballistics experts say not necessarily. High powered shots can sometimes go through things without them even moving. People can react randomly, going into the line of the shot or against it. This alone is not enough evidence to suggest a second shot from the front right. The wound seen in the Zapruder film is an exit wound, the entry point is at the back of Kennedy's head, directly in line with the view from the sixth floor window of the School Book Depository.
2) Ruby shoots Oswald two days after the assassination, surely he was cleaning up the whole operation so that Oswald could not speak of a conspiracy?
Ruby was a hot head, he wasn't 'playing with a full deck'. He was so incensed that Oswald had shot Kennedy that he saw it as his duty to kill the killer. The scene in Oliver Stone's JFK movie, in which Ruby is seen dropping the pristine bullet on the stretcher in the hospital, is pure fiction.
3) The back wound in JFK is too low to create a downward trajectory through the neck. (Thus there were more than three shots.) This is the Magic Bullet theory. Oliver Stone's JFK movie describes a zigzagging bullet which stands in the air for 1.6 seconds before continuing its path into Connally.
The magic bullet, using latest computer simulations, does tie in with the wounds if you take into account where Connally and Kennedy were actually sitting in the car: Connally was not straight in front of Kennedy, as seen in the Oliver Stone JFK movie, Connally was in front and to Kennedy's left, and 3 inches lower. There is, indeed, a direct line path for the bullet from the School Book Depository window if these positions are used.
4) Governor Connally's obvious reaction to a shot 1.6 seconds after President Kennedy was first hit, combined with his strong testimony that he was hit separately.
This simply is not true. There was no 1.6 second delay. Connally and JFK reacted together: see Frame 232 in the Zapruder film.
5) JFK's wound in the front of the throat was repeatedly called a 'wound of entry' by the doctors in Dallas but Oswald was in the School Book Depository, behind.
6) Magic (Miracle) Bullet: The unbelievably small damage to CE 399, the bullet that allegedly created seven wounds in two bodies. There is no way that one bullet can pass through two bodies, create seven wounds, break two bones, and emerge virtually unscathed. So all that damage must have been done by more than one bullet - hence a conspiracy as Oswald could only have fired 3 shots.
See also notes to point 3 above. The almost pristine bullet is consistent with the type of bullet the Carcarno gun uses. The bullet is intended to not deform, and it only hit a small bone in Connally's wrist. There is evidence that a piece of the bullet matches a deposit found in Connally body.
7) The wound in the back of the head seen by the full medical staff at Parkland and some at Bethesda, are not shown by the official photos or X-rays.
8) Shots from the grassy knoll were heard by so many witnesses.
(See point 16 below)
9) The incredible feat of firing three shots in six seconds at a moving target with an inaccurate rifle that had not been practiced with in months. If the FBI's best couldn't do it, how could Oswald?
The Zapruder film shows that it wasn't 6 seconds at all, it was 8.3 seconds, more than enough time to fire off the three shots. Oswald was a champion shot: At 200 yards and whilst rapidly firing when training with the Marines, he had a 48/49 out of 50 accuracy rating which is superb. Kennedy was only 88 yards away.
10) Who could have arranged for the route - The Oliver Stone movie, JFK, says that government level forces must have been involved in arranging for the route - a very strange route in which the car had to decelerate in a type of corner with buildings and open windows all around?
11) The shots from the School Book Depository 6th Floor Window would have to have been shot through thick foliage.
The simulation shown in this documentary shows Kennedy appearing from behind the tree at c88 yards from the assassins bullet. In this simulation the president can clearly be seen.
12) Acoustic evidence, which was used by the Senate investigation, seems to show four bangs heard through an open microphone on a policeman's motorbike. Oswald did not have enough time to fire four shots, and thus it must be a conspiracy.
Firstly the audio recording is not a very clean recording, there is lots of static. This acoustic evidence only works if the policeman is in a very small area - this position is crucial to the theory used in the evidence to the Senate Committee. The documentary shows that the policeman was not in a ring required for the theory to be accurate and, thus, although the theory used is right, the position the policeman is required to be in for the theory to be accurate isn't.
13) The Warren Commission report is a fraud. Over 70% of US citizens said to disbelieve it.
25,000 witnesses, 3000 pieces of evidence. Ambitious 32 year old lawyers on the committee who would have loved nothing better than to expose a conspiracy. The only real error they made was that they failed to consider that Castro could have been behind Oswald. This was because the Warren Commission did not know of the reasons behind newspaper reports that Castro had said he would retaliate for attempts to kill him (Robert Kennedy had secretly ordered the removal of Castro and his government).
14) Conspiracy of silence...
It's now been 40 years and nobody has come out to claim responsibility despite many cases where organised crime has made deals with the authorities. The USA is an open society, such a scheme could not have been kept this secret for so long.
15) The guard in the front left of the car fired the fatal head shot to Kennedy's brain... (Thanks to a reader who sent this in.)
Various frames from the Zapruder film seem to show the guard in the front of the car pulling a gun at exactly the time of the shot to Kennedy's brain...
This is a trick of the light. If you look closely at an untampered piece of the Zapruder film, below, the thing that looks like a gun is actually the sun reflecting off the head of the guy sitting to the alleged gunman's right... The apparent arm is actually from a while line inside the car. Below is Zapruder frame number 316.
16) Is this a picture of a man shooting from behind the fence on the grassy knoll?
Orville Nix was also making a film of the fateful event in Dealy Plaza. But did he catch a man with a badge behind the fence in the grassy knoll?
Experts suggest that this explanation needs quite a lot of imagination - the images could easily be blurred trees, twigs or branches.
17) OK, the Badge Man is just trees and twigs, I get that. But look... Is that a Black dog sitting on a plinth in a picture over there? Stran-ge!
Below is some analysis by Jerry Organ regarding a mysterious figure seen behind the grassy knoll fence. This is the Black Dog Man figure. What does it show? Is it just a tourist(s) watching on? Is it just a black dog? No gun is visible. The images are taken from his excellent analysis at http://mcadams.posc.mu.edu/organ3.htm
18) Is that an umbrella to Kennedy's right while he is being shot? Surely that's suspicious? It isn't even raining!
After investigations, it transpires that 'Umbrella Man' is making a strange political protest and is nothing to do with the assassination in progress... It had been raining shortly before the president's motorcade arrived...
Useful resources: The Zapruder Film frame by frame
The Kennedy Assassination - Beyond Conspiracy a BBC documentary: