Deliberate mistake: The fossilised dog looks like the dog did when he was young; it should look old and decrepit, as the dog was when he died. (Presumably deliberate, to avoid a spoiler.).
Continuity mistake: The lava is close to the machine, until Fry runs to it, then it's a long way away.
Continuity mistake: When Amy and Leela are wrestling, Amy's leotard changes several times. It varies between pink knee-length leggings and no leggings at all.
Factual error: During the flashback of 2000, Fry's family is watching the Rose Bowl. Fry's mom, a Wisconsin fan, shouts "touchdown!" Then we see the score on the TV. Wisconsin 9. Standford 3. 2nd Quarter. However, Wisconsin never led 9-3 and didn't score a TD until the 3rd quarter. It was Standford that had the 9-3 lead in the 2nd quarter.
Answer: You are thinking about episode 20 of series 2 - "Anthology of Interest I". She technically never kills anyone, but in the episode she ask a "What if machine" (one of the Professor's inventions) what would happen if she was more impulsive. The machine then shows the more impulsive Leela killing off the Professor to get the money from his will and thereafter killing Hermes, Bender, Scruffy, Cubert, Nibler, Amy and Zoidberg to cover it up. Finally she does something really impulsive with Fry.
Andreas[DK]