I can believe that Oswald might have taken a few shots at the motorcade, but I don't believe he was the only person in Dallas assigned to kill Kennedy. It's a fact that he deliberately took a menial job at one of the prime locations for a sniper's nest in Dealey Plaza. Oswald did have marksmanship training in the Marines and held a serious grudge against Kennedy for his Cuban and Russian policies.
Having said all that, I believe Oswald was duped into believing he was the sole person responsible for carrying out the assassination. Whoever orchestrated the hit probably assigned another team to make sure the job was done right and Oswald didn't nerve out at the last minute. One of these men was hiding near the grassy knoll, probably in a Ghillie suit to look like the ground. He wouldn't necessarily have to run away during the ensuing chaos- he probably sat perfectly still until he could slip out unnoticed.
There were men at the scene claiming to be officials from the FBI and CIA who were never seen again or interrogated. They were observed picking up shell casings and bullet fragments.
I've also had problems believing the fatal headshot footage. Zapruder jerked his arm four times during the shooting, which was an involuntary reaction to the sound of gunfire. Kennedy's reaction to the fatal shot could just as easily be explained as a front entry wound. Photos exist showing smoke rising from the grassy knoll area, plus several eyewitnesses said they heard at least one shot from that direction.
In my opinion, two separate entities formed two separate plans to assassinate Kennedy that day, but only one team was in place in time to do it. The Mafia had the will and the personnel, but the precision of the shots and the ensuing cover up points to a military operation.