Continuity mistake: When Peter enters the cockpit and accidentally kills the pilots the cockpit looks small enough so that it could only fit Peter and the pilots in their seats. However, when he turns around to leave the cockpit looks big enough to fit an entire group of people.
Continuity mistake: When Karen Black is first shown, her blue uniform is sleeveless, showing her white shirtsleeves. After a cut to the "Dawson's Creek" kids, Peter says "It was a movie in the seventies," and Black's outfit has sleeves. Later, when she is helping people off the plane, her uniform once again is sleeveless.
Plot hole: As evidenced by the big bar room shootout, even if they couldn't die in this episode, wounds would still show up on your body (if shot with a gun, there would still be a hole). So, when Peter jumped off the building, when he hit the ground he should have been reduced to a fleshy puddle, even if he weren't dead.