Although Halley's Comet is visible to the eye during its periodic visits to the inner solar system, it does not appear to the naked eye as a huge ball of fire, as portrayed in "End of the World".
According to the Halley family, their name is actually pronounced Hall-Lee not Hail-Lee.
Midway through the episode, as technicians enter the time tunnel, they leave vertical shadows on the rear of the tunnel, thus revealing that the back end of the tunnel is a painting.
The shadow of some equipment (possibly the boom mic) appears on the wall behind Tony when he first confronts the sheriff.
No astronomer in 1910 could possibly have miscalculated a collision with Halley's Comet. Even at its closest, it was nearly 14 million miles from Earth.
If, as this story suggests, it was believed in 1910 that Halley's comet was heading straight to destroy earth, there would have been contemporaneous records of an impending tragedy by way of newspapers, radio broadcasts, etc, which would have been accessible today (or at least in 1966 when this was made). There aren't any in existence, so the story of such an historical scenario does not make sense.
The first recorded appearance of Halley's comet was around 239 BC, not in 1531 AD as stated by Dr. Swain.