It's not at all clear that Oswald was even involved. It's far more likely that he was on the first floor the entire time, where we was seen minutes before and minutes after the shooting.
We now have video evidence showing that he was not in the window just 5 seconds before the shooting began.
He was seen on the first floor no more than 3 minutes after the shooting took place, and the police officer who saw him insisted that he was not out of breath and did not appear to have just run down six flights of stairs.
The chain of evidence for the bullets is flimsy.
And perhaps most importantly: there is no evidence that Oswald was capable of doing this shooting. He was a mediocre shot as a marine, and no evidence that he dedicated himself to long-range training in the intervening years.
The rifle was not in good shape, and wasn't a very good rifle to begin with.
I don't think there's anywhere near enough evidence to convict Oswald beyond a reasonable doubt, though I also admit that I'm not sure what exactly did happen on the plaza that day.
edit: Thinking about those downvoting without commenting - just one thing I want to implore: in our system of justice, we demand proof of built beyond a reasonable doubt. I think that there are dozens of reasonable doubts about Oswald's involvement; I have outlined three (what we know of his whereabouts during the events in question, the chain of custody for the evidence, and the matter of whether he was even capable of the act). If you honestly think that you can look someone against whom there is similar evidence and pronounce them guilty, I'd love to hear your comments on the matter and what specifically you think proves him guilty beyond a reasonable doubt. This man died without getting a trial; we owe it to our justice system to take a measured approach about the evidence against him.