I think there are three pillars of the Oswald couldn't have done it argument. One is he couldn't have done all of the shots because he wasn't a good marksman. Another he couldn't have fired all the rounds in the time the shots were done. And the third was his ability to go home, kill the officer and get to the theater in the time it would have taken to make all of the trips walking.
I have seen that there are still arguments on both side in the shooting and it's difficult for me to make up my mind.
On the movements, the History or Discovery channel did reenactments of his movements and showed that it was physically possible.