The two parts that make it hard to believe Oswald acted alone:

1) The head shot, which appeared to come from the front

2) The volume of fire - Oswald was an average shot and to get (at the least) three shots off at that distance (two of which could be perceived as mortal) in such a short time span with such a clumsy rifle seems pretty extraordinary.

As it stands, the proof isn't overwhelming for either case and I have always thought Oswald didn't act alone, although I have never fully believed that it was some far-reaching conspiracy either.